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mm/src/code/sys_math3d.c

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// Headers are currently valued at 60 mod 256 (./tools/calc_bss.sh <headers>)
#include "z64math.h"
#include "stdbool.h"
#include "PR/gu.h"
#include "macros.h"
#pragma increment_block_number "n64-us:124"
// The bss index at this point should be 184
Vec3f gZeroVec3f = { 0.0f, 0.0f, 0.0f };
Vec3s gZeroVec3s = { 0, 0, 0 };
f32 Math3D_Normalize(Vec3f* vec) {
f32 magnitude = Math3D_Vec3fMagnitude(vec);
if (IS_ZERO(magnitude)) {
return 0.0f;
}
vec->x *= 1.0f / magnitude;
vec->y *= 1.0f / magnitude;
vec->z *= 1.0f / magnitude;
return magnitude;
}
/**
* Creates an infinite line along the intersection of the plane defined from `planeAA`x + `planeAB`y + `planeAB`z +
* `planeADist` = 0 and `planeBA`x + `planeBB`y + `planeBC`z + `planeBDist` = 0, and finds the closest point on that
* intersection to the line segment `linePointA and linePointB`, outputs the intersection to `closestPoint`
*/
s32 Math3D_PlaneVsLineSegClosestPoint(f32 planeAA, f32 planeAB, f32 planeAC, f32 planeADist, f32 planeBA, f32 planeBB,
f32 planeBC, f32 planeBDist, Vec3f* linePointA, Vec3f* linePointB,
Vec3f* closestPoint) {
static InfiniteLine sPlaneIntersectLine;
static Linef sPlaneIntersectSeg;
Vec3f sp34; // unused
if (!Math3D_PlaneVsPlaneNewLine(planeAA, planeAB, planeAC, planeADist, planeBA, planeBB, planeBC, planeBDist,
&sPlaneIntersectLine)) {
// The planes are parallel
return false;
}
// create a line segment on the plane.
Math_Vec3f_Copy(&sPlaneIntersectSeg.a, &sPlaneIntersectLine.point);
sPlaneIntersectSeg.b.x = (sPlaneIntersectLine.dir.x * 100.0f) + sPlaneIntersectLine.point.x;
sPlaneIntersectSeg.b.y = (sPlaneIntersectLine.dir.y * 100.0f) + sPlaneIntersectLine.point.y;
sPlaneIntersectSeg.b.z = (sPlaneIntersectLine.dir.z * 100.0f) + sPlaneIntersectLine.point.z;
// closestPoint is a point on planeIntersect, sp34 is a point on linePointA, linePointB
if (!Math3D_LineSegMakePerpLineSeg(&sPlaneIntersectSeg.a, &sPlaneIntersectSeg.b, linePointA, linePointB,
closestPoint, &sp34)) {
return false;
}
return true;
}
/**
* Finds the two points on lines A and B where the lines are closest together.
*/
s32 Math3D_LineSegMakePerpLineSeg(Vec3f* lineAPointA, Vec3f* lineAPointB, Vec3f* lineBPointA, Vec3f* lineBPointB,
Vec3f* lineAClosestToB, Vec3f* lineBClosestToA) {
f32 magSq;
f32 scaleB;
f32 lineAx = lineAPointB->x - lineAPointA->x;
f32 lineAy = lineAPointB->y - lineAPointA->y;
f32 lineAz = lineAPointB->z - lineAPointA->z;
f32 lineBx = lineBPointB->x - lineBPointA->x;
f32 lineBy = lineBPointB->y - lineBPointA->y;
f32 lineBz = lineBPointB->z - lineBPointA->z;
f32 compAAlongB;
f32 compBAAlongB;
Vec3f lineAPerpB;
Vec3f lineBAPerpB;
f32 tA;
f32 tB;
magSq = SQ(lineBx) + SQ(lineBy) + SQ(lineBz);
if (IS_ZERO(magSq)) {
return false;
}
scaleB = 1.0f / magSq;
compAAlongB = ((lineAx * lineBx) + (lineAy * lineBy) + (lineAz * lineBz)) * scaleB;
compBAAlongB = ((lineBx * (lineAPointA->x - lineBPointA->x)) + (lineBy * (lineAPointA->y - lineBPointA->y)) +
(lineBz * (lineAPointA->z - lineBPointA->z))) *
scaleB;
lineAPerpB.x = lineAx - (lineBx * compAAlongB);
lineAPerpB.y = lineAy - (lineBy * compAAlongB);
lineAPerpB.z = lineAz - (lineBz * compAAlongB);
magSq = SQXYZ(lineAPerpB);
if (IS_ZERO(magSq)) {
return false;
}
lineBAPerpB.x = (lineAPointA->x - lineBPointA->x) - (lineBx * compBAAlongB);
lineBAPerpB.y = (lineAPointA->y - lineBPointA->y) - (lineBy * compBAAlongB);
lineBAPerpB.z = (lineAPointA->z - lineBPointA->z) - (lineBz * compBAAlongB);
tA = -DOTXYZ(lineAPerpB, lineBAPerpB) / magSq;
lineAClosestToB->x = (lineAx * tA) + lineAPointA->x;
lineAClosestToB->y = (lineAy * tA) + lineAPointA->y;
lineAClosestToB->z = (lineAz * tA) + lineAPointA->z;
tB = (compAAlongB * tA) + compBAAlongB;
lineBClosestToA->x = (lineBx * tB) + lineBPointA->x;
lineBClosestToA->y = (lineBy * tB) + lineBPointA->y;
lineBClosestToA->z = (lineBz * tB) + lineBPointA->z;
return true;
}
/**
* Determines the closest point on the line `line` to `pos`, by forming a line perpendicular from
* `point` to `line` closest point is placed in `closestPoint`
*/
f32 Math3D_LineClosestToPoint(InfiniteLine* line, Vec3f* pos, Vec3f* closestPoint) {
f32 dirMagnitudeSq = Math3D_Vec3fMagnitudeSq(&line->dir);
f32 t;
if (IS_ZERO(dirMagnitudeSq)) {
Math_Vec3f_Copy(closestPoint, pos);
//! @bug Missing early return
}
t = (((pos->x - line->point.x) * line->dir.x) + ((pos->y - line->point.y) * line->dir.y) +
((pos->z - line->point.z) * line->dir.z)) /
dirMagnitudeSq;
closestPoint->x = (line->dir.x * t) + line->point.x;
closestPoint->y = (line->dir.y * t) + line->point.y;
closestPoint->z = (line->dir.z * t) + line->point.z;
return t;
}
void Math3D_FindPointOnPlaneIntersect(f32 planeAAxis1Norm, f32 planeAAxis2Norm, f32 planeBAxis1Norm,
f32 planeBAxis2Norm, f32 axis3Direction, f32 planeADist, f32 planeBDist,
f32* axis1Point, f32* axis2Point) {
*axis1Point = ((planeAAxis2Norm * planeBDist) - (planeBAxis2Norm * planeADist)) / axis3Direction;
*axis2Point = ((planeBAxis1Norm * planeADist) - (planeAAxis1Norm * planeBDist)) / axis3Direction;
}
/**
* Creates a line between the intersections of two planes defined from `planeAA`x + `planeAB`y + `planeAC`z +
* `planeADist` = 0 and `planeBA`x + `planeBB`y + `planeBC`z + `planeBDist` = 0, and outputs the line to `intersect`.
* Returns false if the planes are parallel.
*/
s32 Math3D_PlaneVsPlaneNewLine(f32 planeAA, f32 planeAB, f32 planeAC, f32 planeADist, f32 planeBA, f32 planeBB,
f32 planeBC, f32 planeBDist, InfiniteLine* intersect) {
s32 pad;
Vec3f planeANormal;
Vec3f planeBNormal;
f32 dirX;
f32 dirY;
f32 dirZ;
VEC_SET(planeANormal, planeAA, planeAB, planeAC);
VEC_SET(planeBNormal, planeBA, planeBB, planeBC);
Math3D_Vec3f_Cross(&planeANormal, &planeBNormal, &intersect->dir);
if (IS_ZERO(intersect->dir.x) && IS_ZERO(intersect->dir.y) && IS_ZERO(intersect->dir.z)) {
// planes are parallel
return false;
}
dirX = fabsf(intersect->dir.x);
dirY = fabsf(intersect->dir.y);
dirZ = fabsf(intersect->dir.z);
if ((dirX >= dirY) && (dirX >= dirZ)) {
Math3D_FindPointOnPlaneIntersect(planeAB, planeAC, planeBB, planeBC, intersect->dir.x, planeADist, planeBDist,
&intersect->point.y, &intersect->point.z);
intersect->point.x = 0.0f;
} else if ((dirY >= dirX) && (dirY >= dirZ)) {
Math3D_FindPointOnPlaneIntersect(planeAC, planeAA, planeBC, planeBA, intersect->dir.y, planeADist, planeBDist,
&intersect->point.z, &intersect->point.x);
intersect->point.y = 0.0f;
} else {
Math3D_FindPointOnPlaneIntersect(planeAA, planeAB, planeBA, planeBB, intersect->dir.z, planeADist, planeBDist,
&intersect->point.x, &intersect->point.y);
intersect->point.z = 0.0f;
}
return true;
}
/**
* Gets the closest point on the line formed from the intersection of of the planes defined from
* `planeAA`x + `planeAB`y + `planeAC`z + `planeADist` = 0 and
* `planeBA`x + `planeBB`y + `planeBC`z + `planeBDist` = 0
* the point on the intersection line closest to `point` is placed in `closestPoint`
* returns false if the planes are parallel.
*/
s32 Math3D_PlaneVsPlaneVsLineClosestPoint(f32 planeAA, f32 planeAB, f32 planeAC, f32 planeADist, f32 planeBA,
f32 planeBB, f32 planeBC, f32 planeBDist, Vec3f* point, Vec3f* closestPoint) {
static InfiniteLine sPlaneIntersect;
if (!Math3D_PlaneVsPlaneNewLine(planeAA, planeAB, planeAC, planeADist, planeBA, planeBB, planeBC, planeBDist,
&sPlaneIntersect)) {
return false;
}
Math3D_LineClosestToPoint(&sPlaneIntersect, point, closestPoint);
return true;
}
/**
* Calculates the point on the line from starting point `v0`, in the direction `dir` scaled by `scale`. Result is placed
* in `ret`
*/
void Math3D_PointOnDirectedLine(Vec3f* v0, Vec3f* dir, f32 scale, Vec3f* ret) {
ret->x = (dir->x * scale) + v0->x;
ret->y = (dir->y * scale) + v0->y;
ret->z = (dir->z * scale) + v0->z;
}
/**
* Splits the line segment from end points `v0` and `v1`, and splits that segment
* by `ratio` of `v0`:`v1`, places the resulting point on the line in `ret`
*/
void Math3D_LineSplitRatio(Vec3f* v0, Vec3f* v1, f32 ratio, Vec3f* ret) {
Vec3f diff;
Math_Vec3f_Diff(v1, v0, &diff);
Math3D_PointOnDirectedLine(v0, &diff, ratio, ret);
}
/**
* Calculates the cosine between vectors `a` and `b`
*/
f32 Math3D_Cos(Vec3f* a, Vec3f* b) {
f32 ret;
Math3D_CosOut(a, b, &ret);
return ret;
}
/**
* Calculates the cosine between vectors `a` and `b` and places the result in `dst`
* returns true if the cosine cannot be calculated because the product of the magnitudes is zero
*/
s32 Math3D_CosOut(Vec3f* a, Vec3f* b, f32* dst) {
f32 magProduct = Math3D_Vec3fMagnitude(a) * Math3D_Vec3fMagnitude(b);
if (IS_ZERO(magProduct)) {
*dst = 0.0f;
return true;
}
*dst = ((a->x * b->x) + (a->y * b->y) + (a->z * b->z)) / magProduct;
return false;
}
/**
* Reflects vector `vec` across the normal vector `normal`, reflection vector is placed in
* `reflVec`
*/
void Math3D_Vec3fReflect(Vec3f* vec, Vec3f* normal, Vec3f* reflVec) {
f32 normScaleY;
Vec3f negVec;
f32 normScaleZ;
f32 normScaleX;
f32 vecDotNorm;
negVec.x = vec->x * -1.0f;
negVec.y = vec->y * -1.0f;
negVec.z = vec->z * -1.0f;
vecDotNorm = Math3D_Cos(&negVec, normal);
normScaleX = normal->x * vecDotNorm;
normScaleY = normal->y * vecDotNorm;
normScaleZ = normal->z * vecDotNorm;
reflVec->x = ((normScaleX + vec->x) + (normScaleX + vec->x)) + negVec.x;
reflVec->y = ((normScaleY + vec->y) + (normScaleY + vec->y)) + negVec.y;
reflVec->z = ((normScaleZ + vec->z) + (normScaleZ + vec->z)) + negVec.z;
}
/**
* Checks if the point (`x`,`y`) is contained within the square formed from (`upperLeftX`,`upperLeftY`) to
* (`lowerRightX`,`lowerRightY`)
*/
s32 Math3D_PointInSquare2D(f32 upperLeftX, f32 lowerRightX, f32 upperLeftY, f32 lowerRightY, f32 x, f32 y) {
if ((x >= upperLeftX) && (x <= lowerRightX) && (y >= upperLeftY) && (y <= lowerRightY)) {
return true;
}
return false;
}
/**
* Checks if the square in the XY planed formed around the circle with center (`centerX`,`centerY`)
* with radius `radius` touches any portion of the square formed around the triangle formed from `v0`, `v1`, and `v2`
*/
s32 Math3D_CirSquareVsTriSquareXY(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 centerX, f32 centerY, f32 radius) {
f32 min;
f32 max;
if (v0->x < v1->x) {
min = v0->x;
max = v1->x;
} else {
min = v1->x;
max = v0->x;
}
if (min > v2->x) {
min = v2->x;
} else if (max < v2->x) {
max = v2->x;
}
if ((centerX < (min - radius)) || ((max + radius) < centerX)) {
return false;
}
if (v0->y < v1->y) {
min = v0->y;
max = v1->y;
} else {
min = v1->y;
max = v0->y;
}
if (min > v2->y) {
min = v2->y;
} else if (max < v2->y) {
max = v2->y;
}
if ((centerY < (min - radius)) || (centerY > (max + radius))) {
return false;
}
return true;
}
/**
* Checks if the square in the YZ planed formed around the circle with center (`centerY`,`centerZ`)
* with radius `radius` touches any portion of the square formed around the triangle formed from `v0`, `v1`, and `v2`
*/
s32 Math3D_CirSquareVsTriSquareYZ(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 centerY, f32 centerZ, f32 radius) {
f32 min;
f32 max;
if (v0->z < v1->z) {
min = v0->z;
max = v1->z;
} else {
min = v1->z;
max = v0->z;
}
if (min > v2->z) {
min = v2->z;
} else if (max < v2->z) {
max = v2->z;
}
if ((centerZ < (min - radius)) || ((max + radius) < centerZ)) {
return false;
}
if (v0->y < v1->y) {
min = v0->y;
max = v1->y;
} else {
min = v1->y;
max = v0->y;
}
if (min > v2->y) {
min = v2->y;
} else if (max < v2->y) {
max = v2->y;
}
if ((centerY < (min - radius)) || ((max + radius) < centerY)) {
return false;
}
return true;
}
/**
* Checks if the square in the ZX planed formed around the circle with center (`centerZ`,`centerX`)
* with radius `radius` touches any portion of the square formed around the triangle formed from `v0`, `v1`, and `v2`
*/
s32 Math3D_CirSquareVsTriSquareZX(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 centerZ, f32 centerX, f32 radius) {
f32 min;
f32 max;
if (v0->x < v1->x) {
min = v0->x;
max = v1->x;
} else {
min = v1->x;
max = v0->x;
}
if (min > v2->x) {
min = v2->x;
} else if (max < v2->x) {
max = v2->x;
}
if ((centerX < (min - radius)) || ((max + radius) < centerX)) {
return false;
}
if (v0->z < v1->z) {
min = v0->z;
max = v1->z;
} else {
min = v1->z;
max = v0->z;
}
if (min > v2->z) {
min = v2->z;
} else if (max < v2->z) {
max = v2->z;
}
if ((centerZ < (min - radius)) || ((max + radius) < centerZ)) {
return false;
}
return true;
}
/**
* Checks if the cube formed around the triangle formed from `v0`, `v1`, and `v2`
* has any portion touching the cube formed around the sphere with center `center`
* and radius of `radius`
*/
s32 Math3D_SphCubeVsTriCube(Vec3f* v0, Vec3f* v1, Vec3f* v2, Vec3f* center, f32 radius) {
f32 min;
f32 max;
if (v0->x < v1->x) {
min = v0->x;
max = v1->x;
} else {
min = v1->x;
max = v0->x;
}
if (min > v2->x) {
min = v2->x;
} else if (max < v2->x) {
max = v2->x;
}
if ((center->x < (min - radius)) || ((max + radius) < center->x)) {
return false;
}
if (v0->z < v1->z) {
min = v0->z;
max = v1->z;
} else {
min = v1->z;
max = v0->z;
}
if (min > v2->z) {
min = v2->z;
} else if (max < v2->z) {
max = v2->z;
}
if ((center->z < (min - radius)) || ((max + radius) < center->z)) {
return false;
}
if (v0->y < v1->y) {
min = v0->y;
max = v1->y;
} else {
min = v1->y;
max = v0->y;
}
if (min > v2->y) {
min = v2->y;
} else if (max < v2->y) {
max = v2->y;
}
if ((center->y < (min - radius)) || ((max + radius) < center->y)) {
return false;
}
return true;
}
/**
* Returns the distance squared between `a` and `b` on a single axis
*/
f32 Math3D_Dist1DSq(f32 a, f32 b) {
return SQ(a) + SQ(b);
}
/**
* Returns the distance between `a` and `b` on a single axis
*/
f32 Math3D_Dist1D(f32 a, f32 b) {
return sqrtf(Math3D_Dist1DSq(a, b));
}
/**
* Returns the distance squared between (`x0`,`y0`) and (`x1`,`x2`)
*/
f32 Math3D_Dist2DSq(f32 x0, f32 y0, f32 x1, f32 y1) {
return Math3D_Dist1DSq(x0 - x1, y0 - y1);
}
/**
* Returns the distance between points (`x0`,`y0`) and (`x1`,`y1`)
*/
f32 Math3D_Dist2D(f32 x0, f32 y0, f32 x1, f32 y1) {
return sqrtf(Math3D_Dist2DSq(x0, y0, x1, y1));
}
/**
* Returns the magnitude (length) squared of `vec`
*/
f32 Math3D_Vec3fMagnitudeSq(Vec3f* vec) {
return SQ(vec->x) + SQ(vec->y) + SQ(vec->z);
}
/**
* Returns the magnitude (length) of `vec`
*/
f32 Math3D_Vec3fMagnitude(Vec3f* vec) {
return sqrtf(Math3D_Vec3fMagnitudeSq(vec));
}
/**
* Returns the distance between `a` and `b` squared.
*/
f32 Math3D_Vec3fDistSq(Vec3f* a, Vec3f* b) {
Vec3f diff;
Math_Vec3f_Diff(a, b, &diff);
return Math3D_Vec3fMagnitudeSq(&diff);
}
/*
* Calculates the distance between points `a` and `b`
*/
f32 Math3D_Vec3f_DistXYZ(Vec3f* a, Vec3f* b) {
return Math_Vec3f_DistXYZ(a, b);
}
/*
* Calculates the distance between `a` and `b`.
*/
f32 Math3D_DistXYZ16toF(Vec3s* a, Vec3f* b) {
Vec3f diff;
diff.x = a->x - b->x;
diff.y = a->y - b->y;
diff.z = a->z - b->z;
return Math3D_Vec3fMagnitude(&diff);
}
static Vec3f sABDiff;
static Vec3f sACDiff;
/**
* Gets the Z portion of the cross product of vectors `a - (`dx`,`dy`,z) and `b` - (`dx`,`dy`,z)
*/
f32 Math3D_Vec3fDiff_CrossZ(Vec3f* a, Vec3f* b, f32 dx, f32 dy) {
return ((a->x - dx) * (b->y - dy)) - ((a->y - dy) * (b->x - dx));
}
/**
* Gets the X portion of the cross product of vectors `a - (x,`dy`,`dz`) and `b` - (x,`dy`,`dz`)
*/
f32 Math3D_Vec3fDiff_CrossX(Vec3f* a, Vec3f* b, f32 dy, f32 dz) {
return ((a->y - dy) * (b->z - dz)) - ((a->z - dz) * (b->y - dy));
}
/**
* Gets the Y portion of the cross product of vectors `a - (`dx`,y,`dz`) and `b` - (`dx`,y,`dz`)
*/
f32 Math3D_Vec3fDiff_CrossY(Vec3f* a, Vec3f* b, f32 dz, f32 dx) {
return ((a->z - dz) * (b->x - dx)) - ((a->x - dx) * (b->z - dz));
}
/**
* Gets the Cross Product of vectors `a` and `b` and places the result in `ret`
*/
void Math3D_Vec3f_Cross(Vec3f* a, Vec3f* b, Vec3f* ret) {
ret->x = (a->y * b->z) - (a->z * b->y);
ret->y = (a->z * b->x) - (a->x * b->z);
ret->z = (a->x * b->y) - (a->y * b->x);
}
/*
* Calculates the normal vector to a surface with sides `vb` - `va` and `vc` - `va`
* outputs the normal to `normal`
*/
void Math3D_SurfaceNorm(Vec3f* va, Vec3f* vb, Vec3f* vc, Vec3f* normal) {
Math_Vec3f_Diff(vb, va, &sABDiff);
Math_Vec3f_Diff(vc, va, &sACDiff);
Math3D_Vec3f_Cross(&sABDiff, &sACDiff, normal);
}
/**
* Creates flags relative to the faces of a cube.
*/
s32 Math3D_PointRelativeToCubeFaces(Vec3f* point, Vec3f* min, Vec3f* max) {
s32 ret = 0;
if (point->x > max->x) {
ret = 1;
} else if (point->x < min->x) {
ret |= 2;
}
if (point->y > max->y) {
ret |= 4;
} else if (point->y < min->y) {
ret |= 8;
}
if (point->z > max->z) {
ret |= 0x10;
} else if (point->z < min->z) {
ret |= 0x20;
}
return ret;
}
/**
* Creates flags of `point` relative to the edges of a cube
*/
s32 Math3D_PointRelativeToCubeEdges(Vec3f* point, Vec3f* min, Vec3f* max) {
s32 ret = 0;
if ((-min->x + max->y) < (-point->x + point->y)) {
ret |= 1;
}
if ((-point->x + point->y) < (-max->x + min->y)) {
ret |= 2;
}
if ((max->x + max->y) < (point->x + point->y)) {
ret |= 4;
}
if ((point->x + point->y) < (min->x + min->y)) {
ret |= 8;
}
if ((-min->z + max->y) < (-point->z + point->y)) {
ret |= 0x10;
}
if ((-point->z + point->y) < (-max->z + min->y)) {
ret |= 0x20;
}
if ((max->z + max->y) < (point->z + point->y)) {
ret |= 0x40;
}
if ((point->z + point->y) < (min->z + min->y)) {
ret |= 0x80;
}
if ((-min->z + max->x) < (-point->z + point->x)) {
ret |= 0x100;
}
if ((-point->z + point->x) < (-max->z + min->x)) {
ret |= 0x200;
}
if ((max->z + max->x) < (point->z + point->x)) {
ret |= 0x400;
}
if ((point->z + point->x) < (min->z + min->x)) {
ret |= 0x800;
}
return ret;
}
/**
* Creates flags for `point` relative to the vertices of a cube
*/
s32 Math3D_PointRelativeToCubeVertices(Vec3f* point, Vec3f* min, Vec3f* max) {
s32 ret = 0;
if ((max->x + max->y + max->z) < (point->x + point->y + point->z)) {
ret = 1;
}
if ((-min->x + max->y + max->z) < (-point->x + point->y + point->z)) {
ret |= 2;
}
if ((-min->x + max->y - min->z) < (-point->x + point->y - point->z)) {
ret |= 4;
}
if ((max->x + max->y - min->z) < (point->x + point->y - point->z)) {
ret |= 8;
}
if ((max->x - min->y + max->z) < (point->x - point->y + point->z)) {
ret |= 0x10;
}
//! @bug: The next 2 conditions are the same check.
if ((-min->x - min->y + max->z) < (-point->x - point->y + point->z)) {
ret |= 0x20;
}
if ((-min->x - min->y + max->z) < (-point->x - point->y + point->z)) {
ret |= 0x40;
}
if ((-min->x - min->y - min->z) < (-point->x - point->y - point->z)) {
ret |= 0x80;
}
return ret;
}
/**
* Checks if a line segment with endpoints `a` and `b` intersect a cube
*/
s32 Math3D_LineVsCube(Vec3f* min, Vec3f* max, Vec3f* a, Vec3f* b) {
static Vec3f sTriVtx0;
static Vec3f sTriVtx1;
static Vec3f sTriVtx2;
static Vec3f sIntersectPoint;
s32 flags[2];
flags[0] = flags[1] = 0;
flags[0] = Math3D_PointRelativeToCubeFaces(a, min, max);
if (!flags[0]) {
return true;
}
flags[1] = Math3D_PointRelativeToCubeFaces(b, min, max);
if (!flags[1]) {
return true;
}
if (flags[0] & flags[1]) {
return false;
}
flags[0] |= (Math3D_PointRelativeToCubeEdges(a, min, max) << 8);
flags[1] |= (Math3D_PointRelativeToCubeEdges(b, min, max) << 8);
if (flags[0] & flags[1]) {
return false;
}
flags[0] |= (Math3D_PointRelativeToCubeVertices(a, min, max) << 0x18);
flags[1] |= (Math3D_PointRelativeToCubeVertices(b, min, max) << 0x18);
if (flags[0] & flags[1]) {
return false;
}
// face 1
sTriVtx0.x = min->x;
sTriVtx0.y = min->y;
sTriVtx0.z = min->z;
sTriVtx1.x = min->x;
sTriVtx1.y = min->y;
sTriVtx1.z = max->z;
sTriVtx2.x = min->x;
sTriVtx2.y = max->y;
sTriVtx2.z = max->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, -1.0f, 0.0f, 0.0f, min->x, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx1.x = min->x;
sTriVtx1.y = max->y;
sTriVtx1.z = max->z;
sTriVtx2.x = min->x;
sTriVtx2.y = max->y;
sTriVtx2.z = min->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, -1.0f, 0.0f, 0.0f, min->x, a, b, &sIntersectPoint,
0)) {
return true;
}
// face 2
sTriVtx0.x = min->x;
sTriVtx0.y = max->y;
sTriVtx0.z = max->z;
sTriVtx1.x = min->x;
sTriVtx1.y = min->y;
sTriVtx1.z = max->z;
sTriVtx2.x = max->x;
sTriVtx2.y = max->y;
sTriVtx2.z = max->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, 1.0f, -max->z, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx0.x = max->x;
sTriVtx0.y = max->y;
sTriVtx0.z = max->z;
sTriVtx2.x = max->x;
//! @bug trVtx1.y should be sTriVtx2.y, prevents a tri on the cube from being checked.
sTriVtx1.y = min->y;
sTriVtx2.z = max->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, 1.0f, -max->z, a, b, &sIntersectPoint,
0)) {
return true;
}
// face 3
sTriVtx1.x = min->x;
sTriVtx1.y = max->y;
sTriVtx1.z = min->z;
sTriVtx2.x = min->x;
sTriVtx2.y = max->y;
sTriVtx2.z = max->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 1.0f, 0.0f, -max->y, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx1.x = max->x;
sTriVtx1.y = max->y;
sTriVtx1.z = min->z;
sTriVtx2.x = min->x;
sTriVtx2.y = max->y;
sTriVtx2.z = min->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 1.0f, 0.0f, -max->y, a, b, &sIntersectPoint,
0)) {
return true;
}
// face 4
sTriVtx0.x = min->x;
sTriVtx0.y = min->y;
sTriVtx0.z = min->z;
sTriVtx1.x = min->x;
sTriVtx1.y = max->y;
sTriVtx1.z = min->z;
sTriVtx2.x = max->x;
sTriVtx2.y = max->y;
sTriVtx2.z = min->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, -1.0f, min->z, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx1.x = max->x;
sTriVtx1.y = max->y;
sTriVtx1.z = min->z;
sTriVtx2.x = max->x;
sTriVtx2.y = min->y;
sTriVtx2.z = min->z;
// face 5
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, 0.0f, -1.0f, min->z, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx1.x = max->x;
sTriVtx1.y = min->y;
sTriVtx1.z = min->z;
sTriVtx2.x = max->x;
sTriVtx2.y = min->y;
sTriVtx2.z = max->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, -1.0f, 0.0f, min->y, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx1.x = max->x;
sTriVtx1.y = min->y;
sTriVtx1.z = max->z;
sTriVtx2.x = min->x;
sTriVtx2.y = min->y;
sTriVtx2.z = max->z;
// face 6
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 0.0f, -1.0f, 0.0f, min->y, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx0.x = max->x;
sTriVtx0.y = max->y;
sTriVtx0.z = max->z;
sTriVtx1.x = max->x;
sTriVtx1.y = min->y;
sTriVtx1.z = min->z;
sTriVtx2.x = max->x;
sTriVtx2.y = max->y;
sTriVtx2.z = min->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 1.0f, 0.0f, 0.0f, -max->x, a, b, &sIntersectPoint,
0)) {
return true;
}
sTriVtx1.x = max->x;
sTriVtx1.y = min->y;
sTriVtx1.z = max->z;
sTriVtx2.x = max->x;
sTriVtx2.y = min->y;
sTriVtx2.z = min->z;
if (Math3D_TriLineIntersect(&sTriVtx0, &sTriVtx1, &sTriVtx2, 1.0f, 0.0f, 0.0f, -max->x, a, b, &sIntersectPoint,
0)) {
return true;
}
return false;
}
/**
* Checks if a line segment with endpoints `a` and `b` intersect a cube
*/
s32 Math3D_LineVsCubeShort(Vec3s* min, Vec3s* max, Vec3s* a, Vec3s* b) {
static Vec3f sMinF;
static Vec3f sMaxF;
static Vec3f sAF;
static Vec3f sBF;
sMinF.x = min->x;
sMinF.y = min->y;
sMinF.z = min->z;
sMaxF.x = max->x;
sMaxF.y = max->y;
sMaxF.z = max->z;
sAF.x = a->x;
sAF.y = a->y;
sAF.z = a->z;
sBF.x = b->x;
sBF.y = b->y;
sBF.z = b->z;
return Math3D_LineVsCube(&sMinF, &sMaxF, &sAF, &sBF);
}
/**
* Rotates the xz plane around the y axis `angle` degrees.
* outputs the plane equation `a``pointOnPlane->x` + 0y + `c``pointOnPlane->z`+`d` = 0
*/
void Math3D_RotateXZPlane(Vec3f* pointOnPlane, s16 angle, f32* a, f32* c, f32* d) {
*a = Math_SinS(angle) * 0x7FFF;
*c = Math_CosS(angle) * 0x7FFF;
*d = -((*a * pointOnPlane->x) + (*c * pointOnPlane->z));
}
/*
* Defines a plane from vertices `va`, `vb`, and `vc`. Normal components are output to
* `nx`, `ny`, and `nz`. Distance from the origin is output to `originDist`
* Satisfies the plane equation NxVx + NyVy + NzVz + D = 0
*/
void Math3D_DefPlane(Vec3f* va, Vec3f* vb, Vec3f* vc, f32* nx, f32* ny, f32* nz, f32* originDist) {
static Vec3f sNormal;
f32 normMagnitude;
f32 normMagInv;
Math3D_SurfaceNorm(va, vb, vc, &sNormal);
normMagnitude = sqrtf(SQ(sNormal.x) + SQ(sNormal.y) + SQ(sNormal.z));
if (!IS_ZERO(normMagnitude)) {
normMagInv = 1.0f / normMagnitude;
*nx = sNormal.x * normMagInv;
*ny = sNormal.y * normMagInv;
*nz = sNormal.z * normMagInv;
*originDist = -((*nx * va->x) + (*ny * va->y) + (*nz * va->z));
} else {
*originDist = 0.0f;
*nz = 0.0f;
*ny = 0.0f;
*nx = 0.0f;
}
}
/*
* Returns the answer to the plane equation with elements specified by arguments.
*/
f32 Math3D_PlaneF(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* pointOnPlane) {
return (nx * pointOnPlane->x) + (ny * pointOnPlane->y) + (nz * pointOnPlane->z) + originDist;
}
/*
* Returns the answer to the plane equation
*/
f32 Math3D_Plane(Plane* plane, Vec3f* pointOnPlane) {
return (plane->normal.x * pointOnPlane->x) + (plane->normal.y * pointOnPlane->y) +
(plane->normal.z * pointOnPlane->z) + plane->originDist;
}
/*
* Calculates the absolute distance from a point `p` to the plane defined as
* `nx`, `ny`, `nz`, and `originDist`
*/
f32 Math3D_UDistPlaneToPos(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* p) {
return fabsf(Math3D_DistPlaneToPos(nx, ny, nz, originDist, p));
}
/*
* Calculates the signed distance from a point `p` to a plane defined as
* `nx`, `ny`, `nz`, and `originDist`
*/
f32 Math3D_DistPlaneToPos(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* p) {
f32 normMagnitude = sqrtf(SQ(nx) + SQ(ny) + SQ(nz));
if (IS_ZERO(normMagnitude)) {
return 0.0f;
}
return Math3D_PlaneF(nx, ny, nz, originDist, p) / normMagnitude;
}
/**
* Checks if the point defined by (`z`,`x`) is within distance of the triangle defined from `v0`,`v1`, and `v2`
*/
s32 Math3D_TriChkPointParaYImpl(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x, f32 detMax, f32 chkDist, f32 ny) {
f32 detv0v1;
f32 detv1v2;
f32 detv2v0;
f32 distToEdgeSq;
f32 chkDistSq;
// first check if the point is within range of the triangle.
if (!Math3D_CirSquareVsTriSquareZX(v0, v1, v2, z, x, chkDist)) {
return false;
}
// check if the point is within `chkDist` units of any vertex of the triangle.
chkDistSq = SQ(chkDist);
if (((SQ(v0->z - z) + SQ(v0->x - x)) < chkDistSq) || ((SQ(v1->z - z) + SQ(v1->x - x)) < chkDistSq) ||
((SQ(v2->z - z) + SQ(v2->x - x)) < chkDistSq)) {
return true;
}
// Calculate the determinant of each face of the triangle to the point.
// If all the of determinants are within abs(`detMax`), return true.
if (((detMax >= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) &&
(detMax >= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) &&
(detMax >= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) {
return true;
}
if (((-detMax <= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) &&
(-detMax <= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) &&
(-detMax <= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) {
return true;
}
if ((fabsf(ny) > 0.5f) && (chkDistSq > 0.0f)) {
// Do a check on each face of the triangle, if the point is within `chkDist` units return true.
if (Math3D_PointDistSqToLineZX(z, x, v0, v1, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
if (Math3D_PointDistSqToLineZX(z, x, v1, v2, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
if (Math3D_PointDistSqToLineZX(z, x, v2, v0, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
}
return false;
}
s32 Math3D_TriChkPointParaYDeterminate(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x, f32 detMax, f32 ny) {
return Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, detMax, 1.0f, ny);
}
s32 Math3D_TriChkPointParaYSlopedY(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x) {
return Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, 1.0f, 0.6f);
}
/**
* Performs the triangle and point check parallel to the Y axis, outputs the y coordinate of the point to `yIntersect`
*/
s32 Math3D_TriChkPointParaYIntersectDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 z,
f32 x, f32* yIntersect, f32 chkDist) {
if (IS_ZERO(ny)) {
return false;
}
if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, chkDist, ny)) {
*yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny;
return true;
}
return false;
}
s32 Math3D_TriChkPointParaYIntersectInsideTri(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist,
f32 z, f32 x, f32* yIntersect, f32 chkDist) {
if (IS_ZERO(ny)) {
return false;
}
if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 0.0f, chkDist, ny)) {
*yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny;
return true;
}
return false;
}
s32 Math3D_TriChkPointParaY(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 ny, f32 z, f32 x) {
if (IS_ZERO(ny)) {
return false;
}
if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, 1.0f, ny)) {
return true;
}
return false;
}
s32 Math3D_TriChkLineSegParaYIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 z,
f32 x, f32* yIntersect, f32 y0, f32 y1) {
f32 pointADist;
f32 pointBDist;
Vec3f planePos;
if (IS_ZERO(ny)) {
return false;
}
planePos.x = x;
planePos.y = y0;
planePos.z = z;
pointADist = Math3D_PlaneF(nx, ny, nz, originDist, &planePos);
planePos.y = y1;
pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, &planePos);
if (((pointADist > 0.0f) && (pointBDist > 0.0f)) || ((pointADist < 0.0f) && (pointBDist < 0.0f))) {
return false;
}
if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 300.0f, 1.0f, ny)) {
*yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny;
return true;
}
return false;
}
s32 Math3D_TriChkPointParaYDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, Plane* plane, f32 z, f32 x, f32 chkDist) {
if (IS_ZERO(plane->normal.y)) {
return false;
}
if (Math3D_TriChkPointParaYImpl(v0, v1, v2, z, x, 0.0f, chkDist, plane->normal.y)) {
return true;
}
return false;
}
s32 Math3D_TriChkPointParaYImplNoCheckRange(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 z, f32 x, f32 detMax, f32 chkDist,
f32 ny) {
f32 detv0v1;
f32 detv1v2;
f32 detv2v0;
f32 distToEdgeSq;
f32 chkDistSq;
// check if the point is within `chkDist` units of any vertex of the triangle.
chkDistSq = SQ(chkDist);
if (((SQ(v0->z - z) + SQ(v0->x - x)) < chkDistSq) || ((SQ(v1->z - z) + SQ(v1->x - x)) < chkDistSq) ||
((SQ(v2->z - z) + SQ(v2->x - x)) < chkDistSq)) {
return true;
}
// Calculate the determinant of each face of the triangle to the point.
// If all the of determinants are within abs(`detMax`), return true.
if (((detMax >= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) &&
(detMax >= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) &&
(detMax >= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) {
return true;
}
if (((-detMax <= (detv0v1 = ((v0->z - z) * (v1->x - x)) - ((v0->x - x) * (v1->z - z)))) &&
(-detMax <= (detv1v2 = ((v1->z - z) * (v2->x - x)) - ((v1->x - x) * (v2->z - z)))) &&
(-detMax <= (detv2v0 = ((v2->z - z) * (v0->x - x)) - ((v2->x - x) * (v0->z - z)))))) {
return true;
}
if ((fabsf(ny) > 0.5f) && (chkDistSq > 0.0f)) {
// Do a check on each face of the triangle, if the point is within `chkDist` units return true.
if (Math3D_PointDistSqToLineZX(z, x, v0, v1, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
if (Math3D_PointDistSqToLineZX(z, x, v1, v2, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
if (Math3D_PointDistSqToLineZX(z, x, v2, v0, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
}
return false;
}
s32 Math3D_TriChkPointParaYNoRangeCheckIntersectInsideTri(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz,
f32 originDist, f32 z, f32 x, f32* yIntersect, f32 chkDist) {
if (IS_ZERO(ny)) {
return false;
}
if (Math3D_TriChkPointParaYImplNoCheckRange(v0, v1, v2, z, x, 0.0f, chkDist, ny)) {
*yIntersect = (((-nx * x) - (nz * z)) - originDist) / ny;
return true;
}
return false;
}
s32 Math3D_TriChkPointParaXImpl(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 y, f32 z, f32 detMax, f32 chkDist, f32 ny) {
f32 detv0v1;
f32 detv1v2;
f32 detv2v0;
f32 distToEdgeSq;
f32 chkDistSq;
// first check if the point is within range of the triangle.
if (!Math3D_CirSquareVsTriSquareYZ(v0, v1, v2, y, z, chkDist)) {
return false;
}
// check if the point is within `chkDist` units of any vertex of the triangle.
chkDistSq = SQ(chkDist);
if (((SQ(v0->y - y) + SQ(v0->z - z)) < chkDistSq) || ((SQ(v1->y - y) + SQ(v1->z - z)) < chkDistSq) ||
((SQ(v2->y - y) + SQ(v2->z - z)) < chkDistSq)) {
return true;
}
// Calculate the determinant of each face of the triangle to the point.
// If all the of determinants are within abs(`detMax`), return true.
if (((detMax >= (detv0v1 = ((v0->y - y) * (v1->z - z)) - ((v0->z - z) * (v1->y - y)))) &&
(detMax >= (detv1v2 = ((v1->y - y) * (v2->z - z)) - ((v1->z - z) * (v2->y - y)))) &&
(detMax >= (detv2v0 = ((v2->y - y) * (v0->z - z)) - ((v2->z - z) * (v0->y - y)))))) {
return true;
}
if (((-detMax <= (detv0v1 = ((v0->y - y) * (v1->z - z)) - ((v0->z - z) * (v1->y - y)))) &&
(-detMax <= (detv1v2 = ((v1->y - y) * (v2->z - z)) - ((v1->z - z) * (v2->y - y)))) &&
(-detMax <= (detv2v0 = ((v2->y - y) * (v0->z - z)) - ((v2->z - z) * (v0->y - y)))))) {
return true;
}
if ((fabsf(ny) > 0.5f) && (chkDistSq > 0.0f)) {
// Do a check on each face of the triangle, if the point is within `chkDist` units return true.
if ((Math3D_PointDistSqToLineYZ(y, z, v0, v1, &distToEdgeSq) != 0) && (distToEdgeSq < chkDistSq)) {
return true;
}
if ((Math3D_PointDistSqToLineYZ(y, z, v1, v2, &distToEdgeSq) != 0) && (distToEdgeSq < chkDistSq)) {
return true;
}
if ((Math3D_PointDistSqToLineYZ(y, z, v2, v0, &distToEdgeSq) != 0) && (distToEdgeSq < chkDistSq)) {
return true;
}
}
return false;
}
s32 Math3D_TriChkPointParaXDeterminate(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 y, f32 z, f32 detMax, f32 nx) {
return Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, detMax, 1.0f, nx);
}
s32 Math3D_TriChkPointParaXIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 y,
f32 z, f32* xIntersect) {
if (IS_ZERO(nx)) {
return false;
}
if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) {
*xIntersect = (((-ny * y) - (nz * z)) - originDist) / nx;
return true;
}
return false;
}
s32 Math3D_TriChkPointParaX(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 y, f32 z) {
if (IS_ZERO(nx)) {
return false;
}
if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) {
return true;
}
return false;
}
s32 Math3D_TriChkLineSegParaXIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 y,
f32 z, f32* xIntersect, f32 x0, f32 x1) {
static Vec3f sPlanePos;
f32 pointADist;
f32 pointBDist;
if (IS_ZERO(nx)) {
return false;
}
sPlanePos.x = x0;
sPlanePos.y = y;
sPlanePos.z = z;
pointADist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos);
sPlanePos.x = x1;
pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos);
if (((pointADist > 0.0f) && (pointBDist > 0.0f)) || ((pointADist < 0.0f) && (pointBDist < 0.0f))) {
return false;
}
if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) {
*xIntersect = (((-ny * y) - (nz * z)) - originDist) / nx;
return true;
}
return false;
}
s32 Math3D_TriChkLineSegParaXDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, Plane* plane, f32 y, f32 z, f32 chkDist) {
if (IS_ZERO(plane->normal.x)) {
return false;
}
if (Math3D_TriChkPointParaXImpl(v0, v1, v2, y, z, 0.0f, chkDist, plane->normal.x)) {
return true;
}
return false;
}
s32 Math3D_TriChkPointParaZImpl(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 x, f32 y, f32 detMax, f32 chkDist, f32 nz) {
f32 detv0v1;
f32 detv1v2;
f32 detv2v0;
f32 distToEdgeSq;
f32 chkDistSq;
if (!Math3D_CirSquareVsTriSquareXY(v0, v1, v2, x, y, chkDist)) {
return false;
}
chkDistSq = SQ(chkDist);
if (((SQ(x - v0->x) + SQ(y - v0->y)) < chkDistSq) || ((SQ(x - v1->x) + SQ(y - v1->y)) < chkDistSq) ||
((SQ(x - v2->x) + SQ(y - v2->y)) < chkDistSq)) {
// Distance from any vertex to a point is less than chkDist
return true;
}
if (((detMax >= (detv0v1 = ((v0->x - x) * (v1->y - y)) - ((v0->y - y) * (v1->x - x)))) &&
(detMax >= (detv1v2 = ((v1->x - x) * (v2->y - y)) - ((v1->y - y) * (v2->x - x)))) &&
(detMax >= (detv2v0 = ((v2->x - x) * (v0->y - y)) - ((v2->y - y) * (v0->x - x)))))) {
return true;
}
if (((-detMax <= (detv0v1 = ((v0->x - x) * (v1->y - y)) - ((v0->y - y) * (v1->x - x)))) &&
(-detMax <= (detv1v2 = ((v1->x - x) * (v2->y - y)) - ((v1->y - y) * (v2->x - x)))) &&
(-detMax <= (detv2v0 = ((v2->x - x) * (v0->y - y)) - ((v2->y - y) * (v0->x - x)))))) {
return true;
}
if (fabsf(nz) > 0.5f && chkDistSq > 0.0f) {
if (Math3D_PointDistSqToLineXY(x, y, v0, v1, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
if (Math3D_PointDistSqToLineXY(x, y, v1, v2, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
if (Math3D_PointDistSqToLineXY(x, y, v2, v0, &distToEdgeSq) && (distToEdgeSq < chkDistSq)) {
return true;
}
}
return false;
}
s32 Math3D_TriChkPointParaZDeterminate(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 y, f32 z, f32 detMax, f32 nx) {
return Math3D_TriChkPointParaZImpl(v0, v1, v2, y, z, detMax, 1.0f, nx);
}
s32 Math3D_TriChkPointParaZIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 x,
f32 y, f32* zIntersect) {
if (IS_ZERO(nz)) {
return false;
}
if (Math3D_TriChkPointParaZImpl(v0, v1, v2, x, y, 300.0f, 1.0f, nz)) {
*zIntersect = (((-nx * x) - (ny * y)) - originDist) / nz;
return true;
}
return false;
}
s32 Math3D_TriChkPointParaZ(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 y, f32 z) {
if (IS_ZERO(nx)) {
return false;
}
if (Math3D_TriChkPointParaZImpl(v0, v1, v2, y, z, 300.0f, 1.0f, nx)) {
return true;
}
return false;
}
s32 Math3D_TriChkLineSegParaZIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, f32 x,
f32 y, f32* zIntersect, f32 z0, f32 z1) {
static Vec3f sPlanePos;
f32 pointADist;
f32 pointBDist;
if (IS_ZERO(nz)) {
return false;
}
sPlanePos.x = x;
sPlanePos.y = y;
sPlanePos.z = z0;
pointADist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos);
sPlanePos.z = z1;
pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, &sPlanePos);
if (((pointADist > 0.0f) && (pointBDist > 0.0f)) || ((pointADist < 0.0f) && (pointBDist < 0.0f))) {
// points on the line segment are on the same side of the plane
return false;
}
if (Math3D_TriChkPointParaZImpl(v0, v1, v2, x, y, 300.0f, 1.0f, nz)) {
*zIntersect = (((-nx * x) - (ny * y)) - originDist) / nz;
return true;
}
return false;
}
s32 Math3D_TriChkLineSegParaZDist(Vec3f* v0, Vec3f* v1, Vec3f* v2, Plane* plane, f32 x, f32 y, f32 chkDist) {
if (IS_ZERO(plane->normal.z)) {
return false;
}
if (Math3D_TriChkPointParaZImpl(v0, v1, v2, x, y, 0.0f, chkDist, plane->normal.z)) {
return true;
}
return false;
}
s32 Math3D_LineSegFindPlaneIntersect(f32 pointADist, f32 pointBDist, Vec3f* pointA, Vec3f* pointB, Vec3f* intersect) {
f32 distDiff = pointADist - pointBDist;
if (IS_ZERO(distDiff)) {
// both points lie on the plane.
*intersect = *pointB;
return false;
}
if (pointADist == 0.0f) {
// pointA is on the plane
*intersect = *pointA;
} else if (pointBDist == 0.0f) {
// pointB is on the plane
*intersect = *pointB;
} else {
// place the point at the intersection point.
Math3D_LineSplitRatio(pointA, pointB, pointADist / distDiff, intersect);
}
return true;
}
/**
* Determines if the line segment from `linePointA` to `linePointB` crosses the plane
* from `nx` + `ny` + `nz` + `originDist` = 0. If fromFront is set, then detection will only
* be true if point A crosses from the front of the plane
*/
s32 Math3D_LineSegVsPlane(f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* linePointA, Vec3f* linePointB,
Vec3f* intersect, s32 fromFront) {
f32 pointADist = Math3D_PlaneF(nx, ny, nz, originDist, linePointA);
f32 pointBDist = Math3D_PlaneF(nx, ny, nz, originDist, linePointB);
if ((pointADist * pointBDist) > 0.0f) {
*intersect = *linePointB;
return false;
}
if (fromFront && (pointADist < 0.0f) && (pointBDist > 0.0f)) {
*intersect = *linePointB;
return false;
}
return Math3D_LineSegFindPlaneIntersect(pointADist, pointBDist, linePointA, linePointB, intersect);
}
/*
* Determines if the line formed by `linePointA` and `linePointB` intersect with Triangle formed from
* vertices `v0`, `v1`, and `v2` with normal vector `nx`, `ny`, and `nz` with plane distance from origin
* `originDist` Outputs the intersection point at to `intersect`
* Returns 1 if the line intersects with the triangle, 0 otherwise
*/
s32 Math3D_TriLineIntersect(Vec3f* v0, Vec3f* v1, Vec3f* v2, f32 nx, f32 ny, f32 nz, f32 originDist, Vec3f* linePointA,
Vec3f* linePointB, Vec3f* intersect, s32 fromFront) {
if (!Math3D_LineSegVsPlane(nx, ny, nz, originDist, linePointA, linePointB, intersect, fromFront)) {
return false;
}
if (((nx == 0.0f) || Math3D_TriChkPointParaX(v0, v1, v2, nx, intersect->y, intersect->z)) &&
((ny == 0.0f) || Math3D_TriChkPointParaY(v0, v1, v2, ny, intersect->z, intersect->x)) &&
((nz == 0.0f) || Math3D_TriChkPointParaZ(v0, v1, v2, nz, intersect->x, intersect->y))) {
return true;
}
*intersect = *linePointB;
return false;
}
/*
* Creates a TriNorm output to `tri`, and calculates the normal vector and plane from vertices
* `va`, `vb`, and `vc`
*/
void Math3D_TriNorm(TriNorm* tri, Vec3f* va, Vec3f* vb, Vec3f* vc) {
tri->vtx[0] = *va;
tri->vtx[1] = *vb;
tri->vtx[2] = *vc;
Math3D_DefPlane(va, vb, vc, &tri->plane.normal.x, &tri->plane.normal.y, &tri->plane.normal.z,
&tri->plane.originDist);
}
/*
* Determines if point `point` lies within `sphere`
*/
s32 Math3D_PointInSph(Sphere16* sphere, Vec3f* point) {
if (Math3D_DistXYZ16toF(&sphere->center, point) < sphere->radius) {
return true;
}
return false;
}
/**
* Determines the distance from point (`x0`,`y0`) to the line formed from (`x1`,`y1`) and (`x2`,`y2`)
* Distance squared is output to `lineLenSq`, returns true if the point perpendicular from (`x0`,`y0`)
* is contained within the segment between (`x1`,`y1`) and (`x2`,`y2`)
*/
s32 Math3D_PointDistSqToLine2DImpl(f32 x0, f32 y0, f32 x1, f32 y1, f32 x2, f32 y2, f32* perpXOut, f32* perpYOut,
f32* lineLenSq) {
f32 perpendicularRatio;
f32 xDiff = x2 - x1;
f32 yDiff = y2 - y1;
f32 distSq = SQ(xDiff) + SQ(yDiff);
s32 ret = false;
if (IS_ZERO(distSq)) {
*lineLenSq = 0.0f;
return false;
}
perpendicularRatio = ((x0 - x1) * xDiff + (y0 - y1) * yDiff) / distSq;
if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) {
ret = true;
}
*perpXOut = (xDiff * perpendicularRatio) + x1;
*perpYOut = (yDiff * perpendicularRatio) + y1;
*lineLenSq = SQ(*perpXOut - x0) + SQ(*perpYOut - y0);
return ret;
}
/**
* Determines the distance from point (`x0`,`y0`) to the line formed from (`x1`,`y1`) and (`x2`,`y2`)
* Distance squared is output to `lineLenSq`, returns true if the point perpendicular from (`x0`,`y0`)
* is contained within the segment between (`x1`,`y1`) and (`x2`,`y2`)
*/
s32 Math3D_PointDistSqToLine2D(f32 x0, f32 y0, f32 x1, f32 y1, f32 x2, f32 y2, f32* lineLenSq) {
f32 perpX;
f32 perpY;
return Math3D_PointDistSqToLine2DImpl(x0, y0, x1, y1, x2, y2, &perpX, &perpY, lineLenSq);
}
s32 Math3D_PointDistSqToLineXY(f32 x0, f32 y0, Vec3f* p1, Vec3f* p2, f32* lineLenSq) {
f32 perpendicularRatio;
f32 xDiff = p2->x - p1->x;
f32 yDiff = p2->y - p1->y;
f32 distSq = SQ(xDiff) + SQ(yDiff);
f32 perpX;
f32 perpY;
s32 ret = false;
if (IS_ZERO(distSq)) {
*lineLenSq = 0.0f;
return false;
}
perpendicularRatio = ((x0 - p1->x) * xDiff + (y0 - p1->y) * yDiff) / distSq;
if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) {
ret = true;
}
perpX = (xDiff * perpendicularRatio) + p1->x;
perpY = (yDiff * perpendicularRatio) + p1->y;
*lineLenSq = SQ(perpX - x0) + SQ(perpY - y0);
return ret;
}
s32 Math3D_PointDistSqToLineYZ(f32 y0, f32 z0, Vec3f* p1, Vec3f* p2, f32* lineLenSq) {
f32 perpendicularRatio;
f32 yDiff = p2->y - p1->y;
f32 zDiff = p2->z - p1->z;
f32 distSq = SQ(yDiff) + SQ(zDiff);
f32 perpY;
f32 perpZ;
s32 ret = false;
if (IS_ZERO(distSq)) {
*lineLenSq = 0.0f;
return false;
}
perpendicularRatio = ((y0 - p1->y) * yDiff + (z0 - p1->z) * zDiff) / distSq;
if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) {
ret = true;
}
perpY = (yDiff * perpendicularRatio) + p1->y;
perpZ = (zDiff * perpendicularRatio) + p1->z;
*lineLenSq = SQ(perpY - y0) + SQ(perpZ - z0);
return ret;
}
s32 Math3D_PointDistSqToLineZX(f32 z0, f32 x0, Vec3f* p1, Vec3f* p2, f32* lineLenSq) {
f32 perpendicularRatio;
f32 zDiff = p2->z - p1->z;
f32 xDiff = p2->x - p1->x;
f32 distSq = SQ(zDiff) + SQ(xDiff);
f32 perpZ;
f32 perpX;
s32 ret = false;
if (IS_ZERO(distSq)) {
*lineLenSq = 0.0f;
return false;
}
perpendicularRatio = ((z0 - p1->z) * zDiff + (x0 - p1->x) * xDiff) / distSq;
if ((perpendicularRatio >= 0.0f) && (perpendicularRatio <= 1.0f)) {
ret = true;
}
perpZ = (zDiff * perpendicularRatio) + p1->z;
perpX = (xDiff * perpendicularRatio) + p1->x;
*lineLenSq = SQ(perpZ - z0) + SQ(perpX - x0);
return ret;
}
/**
* Determines if the line `line` is touching the sphere `sphere` at any point in the line.
*/
s32 Math3D_LineVsSph(Sphere16* sphere, Linef* line) {
static Vec3f sSphLinePerpendicularPoint;
Vec3f lineDiff;
f32 temp_f0_2;
f32 lineLenSq;
if ((Math3D_PointInSph(sphere, &line->a)) || (Math3D_PointInSph(sphere, &line->b))) {
// either point of the line is in the sphere.
return true;
}
lineDiff.x = line->b.x - line->a.x;
lineDiff.y = line->b.y - line->a.y;
lineDiff.z = line->b.z - line->a.z;
lineLenSq = SQ(lineDiff.x) + SQ(lineDiff.y) + SQ(lineDiff.z);
if (IS_ZERO(lineLenSq)) {
// line length is "0"
return false;
}
temp_f0_2 = ((((sphere->center.x - line->a.x) * lineDiff.x) + ((sphere->center.y - line->a.y) * lineDiff.y)) +
((sphere->center.z - line->a.z) * lineDiff.z)) /
lineLenSq;
if ((temp_f0_2 < 0.0f) || (temp_f0_2 > 1.0f)) {
return false;
}
sSphLinePerpendicularPoint.x = (lineDiff.x * temp_f0_2) + line->a.x;
sSphLinePerpendicularPoint.y = (lineDiff.y * temp_f0_2) + line->a.y;
sSphLinePerpendicularPoint.z = (lineDiff.z * temp_f0_2) + line->a.z;
if ((SQ(sSphLinePerpendicularPoint.x - sphere->center.x) + SQ(sSphLinePerpendicularPoint.y - sphere->center.y) +
SQ(sSphLinePerpendicularPoint.z - sphere->center.z)) <= SQ((f32)sphere->radius)) {
return true;
}
return false;
}
/**
* Gets the surface point of `sphere` intersecting with `tri` generated from the line formed from the
* sphere's surface to the midpoint of the line formed from the first two vertices of the tri
*/
void Math3D_GetSphVsTriIntersectPoint(Sphere16* sphere, TriNorm* tri, Vec3f* intersectPoint) {
static Vec3f sV0V1Center;
static Vec3f sSphereCenter;
f32 dist;
f32 splitRatio;
sV0V1Center.x = (tri->vtx[0].x + tri->vtx[1].x) * 0.5f;
sV0V1Center.y = (tri->vtx[0].y + tri->vtx[1].y) * 0.5f;
sV0V1Center.z = (tri->vtx[0].z + tri->vtx[1].z) * 0.5f;
sSphereCenter.x = sphere->center.x;
sSphereCenter.y = sphere->center.y;
sSphereCenter.z = sphere->center.z;
dist = Math3D_Vec3f_DistXYZ(&sV0V1Center, &sSphereCenter);
// Distance from the sphere's center to the center of the line formed from v0->v1
if (IS_ZERO(dist)) {
intersectPoint->x = sSphereCenter.x;
intersectPoint->y = sSphereCenter.y;
intersectPoint->z = sSphereCenter.z;
return;
}
splitRatio = sphere->radius / dist;
Math3D_LineSplitRatio(&sSphereCenter, &sV0V1Center, splitRatio, intersectPoint);
}
/**
* Determines if `sphere` and `tri` and touching, and outputs the intersection point to `intersectPoint`
*/
s32 Math3D_TriVsSphIntersect(Sphere16* sphere, TriNorm* tri, Vec3f* intersectPoint) {
static Linef sTriTestLine;
static Vec3f sSphereCenter;
static Vec3f sSphPlanePos;
f32 radius;
f32 nx;
f32 ny;
f32 nz;
f32 planeDist;
sSphereCenter.x = sphere->center.x;
sSphereCenter.y = sphere->center.y;
sSphereCenter.z = sphere->center.z;
radius = sphere->radius;
if (!Math3D_SphCubeVsTriCube(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], &sSphereCenter, radius)) {
return false;
}
planeDist = Math3D_UDistPlaneToPos(tri->plane.normal.x, tri->plane.normal.y, tri->plane.normal.z,
tri->plane.originDist, &sSphereCenter);
if (radius < planeDist) {
// the point that lies within the plane of the triangle which is perpendicular to the sphere's center is more
// than the radius of the sphere, the plane never crosses the sphere.
return false;
}
// tests if any of the edges of the triangle are intersecting the sphere
sTriTestLine.a = tri->vtx[0];
sTriTestLine.b = tri->vtx[1];
if (Math3D_LineVsSph(sphere, &sTriTestLine)) {
Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint);
return true;
}
sTriTestLine.a = tri->vtx[1];
sTriTestLine.b = tri->vtx[2];
if (Math3D_LineVsSph(sphere, &sTriTestLine)) {
Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint);
return true;
}
sTriTestLine.a = tri->vtx[2];
sTriTestLine.b = tri->vtx[0];
if (Math3D_LineVsSph(sphere, &sTriTestLine)) {
Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint);
return true;
}
nx = tri->plane.normal.x * planeDist;
ny = tri->plane.normal.y * planeDist;
nz = tri->plane.normal.z * planeDist;
if (Math3D_PlaneF(tri->plane.normal.x, tri->plane.normal.y, tri->plane.normal.z, tri->plane.originDist,
&sSphereCenter) > 0.0f) {
sSphPlanePos.x = sSphereCenter.x - nx;
sSphPlanePos.y = sSphereCenter.y - ny;
sSphPlanePos.z = sSphereCenter.z - nz;
} else {
sSphPlanePos.x = sSphereCenter.x + nx;
sSphPlanePos.y = sSphereCenter.y + ny;
sSphPlanePos.z = sSphereCenter.z + nz;
}
if (fabsf(tri->plane.normal.y) > 0.5f) {
if (Math3D_TriChkPointParaYDeterminate(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], sSphPlanePos.z, sSphPlanePos.x,
0.0f, tri->plane.normal.y)) {
Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint);
return true;
}
} else if (fabsf(tri->plane.normal.x) > 0.5f) {
if (Math3D_TriChkPointParaXDeterminate(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], sSphPlanePos.y, sSphPlanePos.z,
0.0f, tri->plane.normal.x)) {
Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint);
return true;
}
} else if (Math3D_TriChkPointParaZDeterminate(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], sSphPlanePos.x,
sSphPlanePos.y, 0.0f, tri->plane.normal.z)) {
Math3D_GetSphVsTriIntersectPoint(sphere, tri, intersectPoint);
return true;
}
return false;
}
/*
* Checks if point `point` is within cylinder `cyl`
* Returns 1 if the point is inside the cylinder, 0 otherwise.
*/
s32 Math3D_PointInCyl(Cylinder16* cyl, Vec3f* point) {
f32 bottom;
f32 top;
f32 x = cyl->pos.x - point->x;
f32 z = cyl->pos.z - point->z;
bottom = (f32)cyl->pos.y + cyl->yShift;
top = cyl->height + bottom;
if ((SQ(x) + SQ(z)) < SQ(cyl->radius) && (bottom < point->y) && (point->y < top)) {
return true;
} else {
return false;
}
}
s32 Math3D_CylVsLineSeg(Cylinder16* cyl, Vec3f* linePointA, Vec3f* linePointB, Vec3f* intersectA, Vec3f* intersectB) {
Vec3f cylToPtA;
Vec3f cylToPtB;
Vec3f ptAToPtB;
f32 fracA;
f32 fracB;
f32 fracBase;
f32 zero;
f32 pad;
f32 cylRadiusSq;
f32 radSqDiff;
f32 distCent2;
f32 dot2AB;
s32 sideIntA;
s32 sideIntB;
s32 intBeyondA;
s32 intBeyondB;
s32 intFlags;
Vec3f intPts[4];
s32 count;
s32 i;
fracA = 0.0f;
fracB = 0.0f;
zero = 0.0f;
intFlags = 0;
//! FAKE:
if (1) {}
if (Math3D_PointInCyl(cyl, linePointA) && Math3D_PointInCyl(cyl, linePointB)) {
// both points are in the cylinder
*intersectA = *linePointA;
*intersectB = *linePointB;
return 2;
}
cylToPtA.x = linePointA->x - cyl->pos.x;
cylToPtA.y = linePointA->y - cyl->pos.y - cyl->yShift;
cylToPtA.z = linePointA->z - cyl->pos.z;
cylToPtB.x = linePointB->x - cyl->pos.x;
cylToPtB.y = linePointB->y - cyl->pos.y - cyl->yShift;
cylToPtB.z = linePointB->z - cyl->pos.z;
Math_Vec3f_Diff(&cylToPtB, &cylToPtA, &ptAToPtB);
cylRadiusSq = SQ(cyl->radius);
/**
* This section checks for intersections with the cylinder's base and top
*/
if (!IS_ZERO(ptAToPtB.y)) {
// fraction of length along AB to reach y = 0
fracBase = -cylToPtA.y / ptAToPtB.y;
if ((fracBase >= 0.0f) && (fracBase <= 1.0f)) {
f32 baseIntX = (ptAToPtB.x * fracBase) + cylToPtA.x;
f32 baseIntZ = (ptAToPtB.z * fracBase) + cylToPtA.z;
if ((SQ(baseIntX) + SQ(baseIntZ)) < cylRadiusSq) {
// adds base intersection point to intPts and sets its flag
intPts[0].x = cyl->pos.x + baseIntX;
intPts[0].y = (f32)cyl->pos.y + cyl->yShift;
intPts[0].z = cyl->pos.z + baseIntZ;
intFlags |= 1;
}
}
// fraction of length along AB to reach y = cyl->height
fracA = (cyl->height - cylToPtA.y) / ptAToPtB.y;
if ((fracA >= 0.0f) && (fracA <= 1.0f)) {
f32 topIntX = ptAToPtB.x * fracA + cylToPtA.x;
f32 topIntZ = ptAToPtB.z * fracA + cylToPtA.z;
if ((SQ(topIntX) + SQ(topIntZ)) < cylRadiusSq) {
// adds top intersection point to intPts and sets its flag
intPts[1].x = cyl->pos.x + topIntX;
intPts[1].y = (f32)cyl->pos.y + cyl->yShift + cyl->height;
intPts[1].z = cyl->pos.z + topIntZ;
intFlags |= 2;
}
}
}
/**
* This section finds the points of intersection of the infinite line containing AB with the side of the infinite
* cylinder containing cyl. Intersection points beyond the bounds of the segment and cylinder are filtered out
* afterward.
*/
radSqDiff = SQXZ(cylToPtA) - cylRadiusSq;
if (!IS_ZERO(2.0f * SQXZ(ptAToPtB))) {
dot2AB = 2.0f * DOTXZ(ptAToPtB, cylToPtA);
if (SQ(dot2AB) < (4.0f * SQXZ(ptAToPtB) * radSqDiff)) {
// Line's closest xz-approach is outside cylinder. No intersections.
return 0;
}
if ((SQ(dot2AB) - (4.0f * SQXZ(ptAToPtB) * radSqDiff)) > zero) {
sideIntA = sideIntB = 1;
} else {
// Line is tangent in xz-plane. At most 1 side intersection.
sideIntA = 1;
sideIntB = 0;
}
distCent2 = sqrtf(SQ(dot2AB) - (4.0f * SQXZ(ptAToPtB) * radSqDiff));
if (sideIntA != 0) {
// fraction of length along AB for side intersection closer to A
fracA = (distCent2 - dot2AB) / (2.0f * SQXZ(ptAToPtB));
}
if (sideIntB != 0) {
// fraction of length along AB for side intersection closer to B
fracB = (-dot2AB - distCent2) / (2.0f * SQXZ(ptAToPtB));
}
} else if (!IS_ZERO(2.0f * DOTXZ(ptAToPtB, cylToPtA))) {
// Used if the line segment is nearly vertical. Unclear what it's calculating.
fracA = -radSqDiff / (2.0f * DOTXZ(ptAToPtB, cylToPtA));
sideIntA = 1;
sideIntB = 0;
} else {
return 0;
}
// checks for intersection points outside the bounds of the segment
if (!sideIntB) {
if ((fracA < 0.0f) || (fracA > 1.0f)) {
return 0;
}
} else {
intBeyondA = (fracA < 0.0f) || (fracA > 1.0f);
intBeyondB = (fracB < 0.0f) || (fracB > 1.0f);
if (intBeyondA && intBeyondB) {
return 0;
}
if (intBeyondA) {
sideIntA = 0;
}
if (intBeyondB) {
sideIntB = 0;
}
}
// checks for intersection points outside the bounds of the cylinder
if ((sideIntA != 0) &&
(((fracA * ptAToPtB.y + cylToPtA.y) < 0.0f) || (cyl->height < (fracA * ptAToPtB.y + cylToPtA.y)))) {
sideIntA = 0;
}
if ((sideIntB != 0) &&
(((fracB * ptAToPtB.y + cylToPtA.y) < 0.0f) || (cyl->height < (fracB * ptAToPtB.y + cylToPtA.y)))) {
sideIntB = 0;
}
if ((sideIntA == 0) && (sideIntB == 0)) {
return 0;
}
// Adds intersection points to intPts and sets side A and side B flags
if (sideIntA != 0 && sideIntB != 0) {
intPts[2].x = (fracA * ptAToPtB.x + cylToPtA.x) + cyl->pos.x;
intPts[2].y = (fracA * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift;
intPts[2].z = (fracA * ptAToPtB.z + cylToPtA.z) + cyl->pos.z;
intFlags |= 4;
intPts[3].x = (fracB * ptAToPtB.x + cylToPtA.x) + cyl->pos.x;
intPts[3].y = (fracB * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift;
intPts[3].z = (fracB * ptAToPtB.z + cylToPtA.z) + cyl->pos.z;
intFlags |= 8;
} else if (sideIntA != 0) {
intPts[2].x = (fracA * ptAToPtB.x + cylToPtA.x) + cyl->pos.x;
intPts[2].y = (fracA * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift;
intPts[2].z = (fracA * ptAToPtB.z + cylToPtA.z) + cyl->pos.z;
intFlags |= 4;
} else if (sideIntB != 0) {
intPts[2].x = (fracB * ptAToPtB.x + cylToPtA.x) + cyl->pos.x;
intPts[2].y = (fracB * ptAToPtB.y + cylToPtA.y) + cyl->pos.y + cyl->yShift;
intPts[2].z = (fracB * ptAToPtB.z + cylToPtA.z) + cyl->pos.z;
intFlags |= 4;
}
/**
* Places the found intersection points into intersectA and intersectB. IntersectA is always closer to point A
*/
for (count = 0, i = 0; i < ARRAY_COUNT(intPts); i++) {
if (intFlags & (1 << i)) {
if (count == 0) {
*intersectA = intPts[i];
} else if (count == 1) {
if (Math3D_Vec3fDistSq(intersectA, linePointA) < Math3D_Vec3fDistSq(intersectA, &intPts[i])) {
*intersectB = intPts[i];
} else {
*intersectB = *intersectA;
*intersectA = intPts[i];
}
break;
}
count++;
}
}
return count;
}
/*
* Determines if `cyl` and `tri` are touching. The point of intersection
* is placed in `intersect` Returns 1 if they are touching, 0 otherwise.
*/
s32 Math3D_CylTriVsIntersect(Cylinder16* cyl, TriNorm* tri, Vec3f* intersect) {
static Sphere16 sTopSphere;
static Sphere16 sBottomSphere;
static Vec3f sCylIntersectA;
static Vec3f sCylIntersectB;
f32 yIntersect;
f32 cylTop;
f32 cylBottom;
f32 minDistSq;
f32 radiusTodistFromCylYIntersectTov0v1;
f32 distFromPointAToIntersectASq;
Vec3f cylIntersectCenter;
cylBottom = (f32)cyl->pos.y + cyl->yShift;
cylTop = cyl->height + cylBottom;
if (((tri->vtx[0].y < cylBottom) && (tri->vtx[1].y < cylBottom) && (tri->vtx[2].y < cylBottom)) ||
((cylTop < tri->vtx[0].y) && (cylTop < tri->vtx[1].y) && (cylTop < tri->vtx[2].y))) {
// If all of the vertices are below or all of the vertices are above the cylinder.
return false;
}
minDistSq = 1.e38f;
if (Math3D_CylVsLineSeg(cyl, &tri->vtx[0], &tri->vtx[1], &sCylIntersectA, &sCylIntersectB)) {
distFromPointAToIntersectASq = Math3D_Vec3fDistSq(&sCylIntersectA, &tri->vtx[0]);
minDistSq = distFromPointAToIntersectASq;
*intersect = sCylIntersectA;
}
if (Math3D_CylVsLineSeg(cyl, &tri->vtx[2], &tri->vtx[1], &sCylIntersectA, &sCylIntersectB)) {
distFromPointAToIntersectASq = Math3D_Vec3fDistSq(&sCylIntersectA, &tri->vtx[2]);
if (distFromPointAToIntersectASq < minDistSq) {
*intersect = sCylIntersectA;
minDistSq = distFromPointAToIntersectASq;
}
}
if (Math3D_CylVsLineSeg(cyl, &tri->vtx[0], &tri->vtx[2], &sCylIntersectA, &sCylIntersectB)) {
distFromPointAToIntersectASq = Math3D_Vec3fDistSq(&sCylIntersectA, &tri->vtx[0]);
if (distFromPointAToIntersectASq < minDistSq) {
*intersect = sCylIntersectA;
minDistSq = distFromPointAToIntersectASq;
}
}
if (minDistSq != 1.e38f) {
return true;
}
if (Math3D_TriChkLineSegParaYIntersect(&tri->vtx[0], &tri->vtx[1], &tri->vtx[2], tri->plane.normal.x,
tri->plane.normal.y, tri->plane.normal.z, tri->plane.originDist, cyl->pos.z,
cyl->pos.x, &yIntersect, cylBottom, cylTop)) {
Vec3f midpointv0v1;
Vec3f diffMidpointIntersect;
f32 distFromCylYIntersectTov0v1;
s32 pad;
cylIntersectCenter.x = cyl->pos.x;
cylIntersectCenter.y = yIntersect;
cylIntersectCenter.z = cyl->pos.z;
midpointv0v1.x = (tri->vtx[0].x + tri->vtx[1].x) * 0.5f;
midpointv0v1.y = (tri->vtx[0].y + tri->vtx[1].y) * 0.5f;
midpointv0v1.z = (tri->vtx[0].z + tri->vtx[1].z) * 0.5f;
Math_Vec3f_Diff(&midpointv0v1, &cylIntersectCenter, &diffMidpointIntersect);
distFromCylYIntersectTov0v1 = sqrtf(SQ(diffMidpointIntersect.x) + SQ(diffMidpointIntersect.z));
if (IS_ZERO(distFromCylYIntersectTov0v1)) {
Math_Vec3f_Copy(intersect, &midpointv0v1);
return true;
}
radiusTodistFromCylYIntersectTov0v1 = cyl->radius / distFromCylYIntersectTov0v1;
Math3D_PointOnDirectedLine(&cylIntersectCenter, &diffMidpointIntersect, radiusTodistFromCylYIntersectTov0v1,
intersect);
return true;
}
sTopSphere.center.x = sBottomSphere.center.x = cyl->pos.x;
sTopSphere.center.z = sBottomSphere.center.z = cyl->pos.z;
sTopSphere.center.y = cylTop;
sBottomSphere.center.y = cylBottom;
sTopSphere.radius = sBottomSphere.radius = cyl->radius;
if (Math3D_TriVsSphIntersect(&sTopSphere, tri, intersect) ||
Math3D_TriVsSphIntersect(&sBottomSphere, tri, intersect)) {
return true;
}
return false;
}
/*
* Determines if `cyl` and `tri` are touching.
*/
s32 Math3D_CylVsTri(Cylinder16* cyl, TriNorm* tri) {
Vec3f intersect;
return Math3D_CylTriVsIntersect(cyl, tri, &intersect);
}
/*
* Determines if two spheres are touching.
*/
s32 Math3D_SphVsSph(Sphere16* sphereA, Sphere16* sphereB) {
f32 overlapSize;
return Math3D_SphVsSphOverlap(sphereA, sphereB, &overlapSize);
}
/*
* Determines if two spheres are touching. The amount that they're overlapping is placed in `overlapSize`
*/
s32 Math3D_SphVsSphOverlap(Sphere16* sphereA, Sphere16* sphereB, f32* overlapSize) {
f32 centerDist;
return Math3D_SphVsSphOverlapCenterDist(sphereA, sphereB, overlapSize, &centerDist);
}
/*
* Determines if two spheres are touching The distance from the centers is placed in `centerDist`,
* and the amount that they're overlapping is placed in `overlapSize`
*/
s32 Math3D_SphVsSphOverlapCenterDist(Sphere16* sphereA, Sphere16* sphereB, f32* overlapSize, f32* centerDist) {
Vec3f diff;
diff.x = (f32)sphereA->center.x - (f32)sphereB->center.x;
diff.y = (f32)sphereA->center.y - (f32)sphereB->center.y;
diff.z = (f32)sphereA->center.z - (f32)sphereB->center.z;
*centerDist = sqrtf(SQ(diff.x) + SQ(diff.y) + SQ(diff.z));
*overlapSize = (((f32)sphereA->radius + (f32)sphereB->radius) - *centerDist);
if (*overlapSize > 0.008f) {
return true;
}
*overlapSize = 0.0f;
return false;
}
/**
* Checks if `sph` and `cyl` are touching, output the amount of xz overlap to `overlapSize`
*/
s32 Math3D_SphVsCylOverlap(Sphere16* sph, Cylinder16* cyl, f32* overlapSize) {
f32 centerDist;
return Math3D_SphVsCylOverlapCenterDist(sph, cyl, overlapSize, &centerDist);
}
/**
* Checks if `sph` and `cyl` are touching, output the xz distance of the centers to `centerDist`, and the amount of
* xz overlap to `overlapSize`
*/
s32 Math3D_SphVsCylOverlapCenterDist(Sphere16* sph, Cylinder16* cyl, f32* overlapSize, f32* centerDist) {
static Cylinderf sCylf;
static Spheref sSphf;
f32 x;
f32 z;
f32 combinedRadius;
f32 cylBottom;
f32 cylTop;
f32 sphBottom;
f32 sphTop;
if ((sph->radius <= 0) || (cyl->radius <= 0)) {
// either radius is 0
return false;
}
sSphf.center.y = sph->center.y;
sSphf.radius = sph->radius;
sCylf.pos.y = cyl->pos.y;
sCylf.yShift = cyl->yShift;
sCylf.height = cyl->height;
x = (f32)sph->center.x - cyl->pos.x;
z = (f32)sph->center.z - cyl->pos.z;
combinedRadius = (f32)sph->radius + cyl->radius;
*centerDist = sqrtf(SQ(x) + SQ(z));
if (combinedRadius < *centerDist) {
// if the combined radii is less than the distance to the centers, they cannot be touching.
return false;
}
cylBottom = (sCylf.pos.y + sCylf.yShift);
cylTop = cylBottom + sCylf.height;
sphBottom = sSphf.center.y - sSphf.radius;
sphTop = sSphf.center.y + sSphf.radius;
if ((sphTop >= cylBottom) && (sphBottom <= cylTop)) {
// if the cylinder and sphere are intersecting on the xz plane, check if they're intersecting on
// the y axis.
*overlapSize = combinedRadius - *centerDist;
return true;
}
return false;
}
/**
* Checks if `ca` and `cb` are touching, output the amount of xz overlap to `overlapSize`
*/
s32 Math3D_CylVsCylOverlap(Cylinder16* ca, Cylinder16* cb, f32* overlapSize) {
f32 centerDist;
return Math3D_CylVsCylOverlapCenterDist(ca, cb, overlapSize, &centerDist);
}
/**
* Checks if `ca` and `cb` are touching, output the xz distance of the centers to `centerDist`, and the amount of
* xz overlap to `overlapSize`
*/
s32 Math3D_CylVsCylOverlapCenterDist(Cylinder16* ca, Cylinder16* cb, f32* overlapSize, f32* centerDist) {
static Cylinderf sCaf;
static Cylinderf sCbf;
Math_Vec3s_ToVec3f(&sCaf.pos, &ca->pos);
sCaf.radius = ca->radius;
sCaf.yShift = ca->yShift;
sCaf.height = ca->height;
Math_Vec3s_ToVec3f(&sCbf.pos, &cb->pos);
sCbf.radius = cb->radius;
sCbf.yShift = cb->yShift;
sCbf.height = cb->height;
*centerDist = sqrtf(SQ(sCaf.pos.x - sCbf.pos.x) + SQ(sCaf.pos.z - sCbf.pos.z));
// The combined radii are within the xz distance
if ((sCaf.radius + sCbf.radius) < *centerDist) {
return false;
}
// top of ca < bottom of cb or top of cb < bottom of ca
if ((((sCaf.pos.y + sCaf.yShift) + sCaf.height) < (sCbf.pos.y + sCbf.yShift)) ||
(((sCbf.pos.y + sCbf.yShift) + sCbf.height) < (sCaf.pos.y + sCaf.yShift))) {
return false;
}
*overlapSize = sCaf.radius + sCbf.radius - *centerDist;
return true;
}
/*
* Determines if triangle `ta` intersects with triangle `tb` the point of
* intersection is output to `intersect.
* Returns true is the triangles intersect, 0 otherwise
*/
s32 Math3D_TriVsTriIntersect(TriNorm* ta, TriNorm* tb, Vec3f* intersect) {
f32 dist0 = Math3D_Plane(&ta->plane, &tb->vtx[0]);
f32 dist1 = Math3D_Plane(&ta->plane, &tb->vtx[1]);
f32 dist2 = Math3D_Plane(&ta->plane, &tb->vtx[2]);
if (((dist0 > 0.0f) && (dist1 > 0.0f) && (dist2 > 0.0f)) ||
(((dist0 < 0.0f) && (dist1 < 0.0f)) && (dist2 < 0.0f))) {
return false;
}
dist0 = Math3D_Plane(&tb->plane, &ta->vtx[0]);
dist1 = Math3D_Plane(&tb->plane, &ta->vtx[1]);
dist2 = Math3D_Plane(&tb->plane, &ta->vtx[2]);
if ((((dist0 > 0.0f) && (dist1 > 0.0f)) && (dist2 > 0.0f)) ||
((dist0 < 0.0f) && (dist1 < 0.0f) && (dist2 < 0.0f))) {
return false;
}
if (Math3D_TriLineIntersect(&tb->vtx[0], &tb->vtx[1], &tb->vtx[2], tb->plane.normal.x, tb->plane.normal.y,
tb->plane.normal.z, tb->plane.originDist, &ta->vtx[0], &ta->vtx[1], intersect, 0)) {
return true;
}
if (Math3D_TriLineIntersect(&tb->vtx[0], &tb->vtx[1], &tb->vtx[2], tb->plane.normal.x, tb->plane.normal.y,
tb->plane.normal.z, tb->plane.originDist, &ta->vtx[1], &ta->vtx[2], intersect, 0)) {
return true;
}
if (Math3D_TriLineIntersect(&tb->vtx[0], &tb->vtx[1], &tb->vtx[2], tb->plane.normal.x, tb->plane.normal.y,
tb->plane.normal.z, tb->plane.originDist, &ta->vtx[2], &ta->vtx[0], intersect, 0)) {
return true;
}
if (Math3D_TriLineIntersect(&ta->vtx[0], &ta->vtx[1], &ta->vtx[2], ta->plane.normal.x, ta->plane.normal.y,
ta->plane.normal.z, ta->plane.originDist, &tb->vtx[0], &tb->vtx[1], intersect, 0)) {
return true;
}
if (Math3D_TriLineIntersect(&ta->vtx[0], &ta->vtx[1], &ta->vtx[2], ta->plane.normal.x, ta->plane.normal.y,
ta->plane.normal.z, ta->plane.originDist, &tb->vtx[1], &tb->vtx[2], intersect, 0)) {
return true;
}
if (Math3D_TriLineIntersect(&ta->vtx[0], &ta->vtx[1], &ta->vtx[2], ta->plane.normal.x, ta->plane.normal.y,
ta->plane.normal.z, ta->plane.originDist, &tb->vtx[2], &tb->vtx[0], intersect, 0)) {
return true;
}
return false;
}
s32 Math3D_XZInSphere(Sphere16* sphere, f32 x, f32 z) {
f32 xDiff = sphere->center.x - x;
f32 zDiff = sphere->center.z - z;
if ((SQ(xDiff) + SQ(zDiff)) <= SQ(sphere->radius)) {
return true;
}
return false;
}
s32 Math3D_XYInSphere(Sphere16* sphere, f32 x, f32 y) {
f32 xDiff = sphere->center.x - x;
f32 yDiff = sphere->center.y - y;
if ((SQ(xDiff) + SQ(yDiff)) <= SQ(sphere->radius)) {
return true;
}
return false;
}
s32 Math3D_YZInSphere(Sphere16* sphere, f32 y, f32 z) {
f32 yDiff = sphere->center.y - y;
f32 zDiff = sphere->center.z - z;
if ((SQ(yDiff) + SQ(zDiff)) <= SQ(sphere->radius)) {
return true;
}
return false;
}
/**
* @brief Computes the intersection points, if any, of the circle of radius radius, center (centerX, centerY) with the
* line through the point (pointX, pointY) in direction (dirX, dirY).
*
* @param[in] centreX x coordinate of centre of circle
* @param[in] centerY y coordinate of centre of circle
* @param[in] radius of circle
* @param[in] pointX x coordinate of point on line
* @param[in] pointY y coordinate of point on line
* @param[in] dirX x value of direction vector of line
* @param[in] dirY y value of direction vecotr of line
* @param[out] intersectAX x coordinate of first intersection
* @param[out] intersectAY y coordinate of first intersection
* @param[out] intersectBX x coordinate of second intersection
* @param[out] intersectBY y coordinate of second intersection
* @return number of intersections(ish)
*/
s32 Math3D_CircleLineIntersections(f32 centreX, f32 centerY, f32 radius, f32 pointX, f32 pointY, f32 dirX, f32 dirY,
f32* intersectAX, f32* intersectAY, f32* intersectBX, f32* intersectBY) {
f32 a = SQ(dirX) + SQ(dirY); // t^2 coefficient, |dir|^2
f32 diffX = pointX - centreX;
f32 diffY = pointY - centerY;
f32 b; // t coefficient
f32 delta; // discriminant of quadratic
f32 rootP; // larger root of quadratic
f32 rootN; // smaller root of quadratic
s32 ret;
// if the direction vector's magnitude is too small, assume no intersections
if ((IS_ZERO(dirX) && IS_ZERO(dirY)) || IS_ZERO(a)) {
*intersectAX = 0.0f;
*intersectAY = 0.0f;
*intersectBX = 0.0f;
*intersectBY = 0.0f;
return 0;
}
b = 2.0f * (dirX * diffX + dirY * diffY); // 2 dir . (point - centre)
delta = SQ(b) - 4.0f * a * (SQ(diffX) + SQ(diffY) - SQ(radius));
ret = 0;
if (IS_ZERO(delta)) { // At most one root if discriminant is close to zero
// This root is always overwritten later.
rootN = -b / (2.0f * a);
*intersectAX = dirX * rootN + pointX;
*intersectAY = dirY * rootN + pointY;
*intersectBX = 0.0f;
*intersectBY = 0.0f;
}
if (delta > 0.0f) { // Two roots if discriminant > 0
rootN = (-b - sqrtf(delta)) / (2.0f * a);
*intersectAX = dirX * rootN + pointX;
*intersectAY = dirY * rootN + pointY;
rootP = (-b + sqrtf(delta)) / (2.0f * a);
*intersectBX = dirX * rootP + pointX;
*intersectBY = dirY * rootP + pointY;
ret = 2;
} else { // "No roots if discriminant <= 0.0f"*
//! @bug Should be one root if discriminant == 0, not zero (although this case is unlikely for floats)
*intersectAX = 0.0f;
*intersectAY = 0.0f;
}
return ret;
}
void func_8017FD44(Vec3f* arg0, Vec3f* arg1, Vec3f* dst, f32 arg3) {
Vec3f sp2C;
s16 sp2A;
f32 sp24;
if ((arg3 < -1.0f) && (arg3 > 1.0f)) {
return;
}
sp2C.x = (arg0->x + arg1->x) / 2.0f;
sp2C.z = (arg0->z + arg1->z) / 2.0f;
sp24 = sqrtf(SQ(sp2C.x - arg0->x) + SQ(sp2C.z - arg0->z));
dst->y = (arg1->y - arg0->y) * arg3 + arg0->y;
sp2A = Math_Vec3f_Yaw(&sp2C, arg0);
dst->x = Math_SinS(TRUNCF_BINANG(0x7FFF * arg3) + sp2A) * sp24 + sp2C.x;
dst->z = Math_CosS(TRUNCF_BINANG(0x7FFF * arg3) + sp2A) * sp24 + sp2C.z;
}
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