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maths.c
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maths.c
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#include "3dc.h"
#include "inline.h"
#include "maths.h"
#define UseTimsPinp Yes
/*
externs for commonly used global variables and arrays
*/
extern const short ArcCosTable[4096];
extern const short ArcSineTable[4096];
extern const short ArcTanTable[256];
extern LONGLONGCH ll_zero;
/*
Globals
*/
MATRIXCH IdentityMatrix = {
ONE_FIXED, 0, 0,
0, ONE_FIXED, 0,
0, 0, ONE_FIXED
};
/*
Maths functions used by the system
*/
/* One over sin functions - CDF 4/2/98 */
extern int oneoversin[4096];
void ConstructOneOverSinTable(void) {
int a,sin;
for (a=0; a<4096; a++) {
sin=GetSin(a);
if (sin!=0) {
oneoversin[a]=DIV_FIXED(ONE_FIXED,sin);
} else {
sin=100;
oneoversin[a]=DIV_FIXED(ONE_FIXED,sin);
}
}
}
int GetOneOverSin(int a) {
int b;
b=a&wrap360;
return(oneoversin[b]);
}
/*
Dot Product Function
It accepts two pointers to vectors and returns an int result
*/
int _DotProduct(VECTORCH *vptr1, VECTORCH *vptr2)
{
int dp;
dp = MUL_FIXED(vptr1->vx, vptr2->vx);
dp += MUL_FIXED(vptr1->vy, vptr2->vy);
dp += MUL_FIXED(vptr1->vz, vptr2->vz);
return(dp);
}
int DotProduct2d(VECTOR2D *vptr1, VECTOR2D *vptr2)
{
int dp;
dp = MUL_FIXED(vptr1->vx, vptr2->vx);
dp += MUL_FIXED(vptr1->vy, vptr2->vy);
return dp;
}
/*
This function returns the distance between two vectors
*/
int VectorDistance(VECTORCH *v1, VECTORCH *v2)
{
VECTORCH v;
v.vx = v1->vx - v2->vx;
v.vy = v1->vy - v2->vy;
v.vz = v1->vz - v2->vz;
return Magnitude(&v);
}
/*
This function compares the distance between two vectors along each of
the major axes and returns Yes or No if they are within the cube defined
by the argument passed.
*/
int OutcodeVectorDistance(VECTORCH *v1, VECTORCH *v2, int d)
{
int i;
i = v1->vx - v2->vx;
if(i < 0) i = -i;
if(i >= d) return No;
i = v1->vy - v2->vy;
if(i < 0) i = -i;
if(i >= d) return No;
i = v1->vz - v2->vz;
if(i < 0) i = -i;
if(i >= d) return No;
return Yes;
}
/*
Subtract one VECTORCH from another and return the result as a normal
v3 = Normal(v1 - v2)
*/
void GetNormalVector(VECTORCH *v1, VECTORCH *v2, VECTORCH *v3)
{
v3->vx = v1->vx - v2->vx;
v3->vy = v1->vy - v2->vy;
v3->vz = v1->vz - v2->vz;
Normalise(v3);
}
/*
Normalise a vector close to, but less than, unit length
*/
void Renormalise(VECTORCH *nvector)
{
int m;
int xsq, ysq, zsq;
/* Scale x, y and z */
nvector->vx >>= 2;
nvector->vy >>= 2;
nvector->vz >>= 2;
/* Normalise */
xsq = nvector->vx * nvector->vx;
ysq = nvector->vy * nvector->vy;
zsq = nvector->vz * nvector->vz;
m = SqRoot32(xsq + ysq + zsq);
if(m == 0) m = 1; /* Just in case */
nvector->vx = (nvector->vx * ONE_FIXED) / m;
nvector->vy = (nvector->vy * ONE_FIXED) / m;
nvector->vz = (nvector->vz * ONE_FIXED) / m;
}
/*
Return the shift value required to get one value LTE the other value
*/
int FindShift32(int value, int limit)
{
int shift = 0;
/*if(limit == 0) exit(0xfa11fa11);*/
if(value < 0) value = -value;
while(value > limit) {
shift++;
value >>= 1;
}
return shift;
}
/*
Return the largest value of an int array
*/
int MaxInt(int *iarray, int iarraysize)
{
int imax = smallint;
int i;
for(i = iarraysize; i!=0; i--) {
if(imax < *iarray) imax = *iarray;
iarray++;
}
return imax;
}
/*
Return the smallest value of an int array
*/
int MinInt(int *iarray, int iarraysize)
{
int imin = bigint;
int i;
for(i = iarraysize; i!=0; i--) {
if(imin > *iarray) imin = *iarray;
iarray++;
}
return imin;
}
/*
Create Matrix from Euler Angles
It requires a pointer to some euler angles and a pointer to a matrix
Construct the matrix elements using the following formula
Formula for ZXY Matrix
m11 = cy*cz + sx*sy*sz m12 = -cy*sz + sx*sy*cz m13 = cx*sy
m21 = cx*sz m22 = cx*cz m23 = -sx
m31 = -sy*cz + sx*cy*sz m32 = sy*sz + sx*cy*cz m33 = cx*cy
*/
void CreateEulerMatrix(EULER *e, MATRIXCH *m1)
{
int t, sx, sy, sz, cx, cy, cz;
sx = GetSin(e->EulerX);
sy = GetSin(e->EulerY);
sz = GetSin(e->EulerZ);
cx = GetCos(e->EulerX);
cy = GetCos(e->EulerY);
cz = GetCos(e->EulerZ);
#if 0
textprint("Euler Matrix Sines & Cosines\n");
textprint("%d, %d, %d\n", sx, sy, sz);
textprint("%d, %d, %d\n", cx, cy, cz);
#endif
/* m11 = cy*cz + sx*sy*sz */
m1->mat11 = MUL_FIXED(cy, cz); /* cy*cz */
t = MUL_FIXED(sx, sy); /* sx*sy */
t = MUL_FIXED(t, sz); /* *sz */
m1->mat11 += t;
/* m12 = -cy*sz + sx*sy*cz */
m1->mat12=MUL_FIXED(-cy,sz);
t=MUL_FIXED(sx,sy);
t=MUL_FIXED(t,cz);
m1->mat12+=t;
/* m13 = cx*sy */
m1->mat13=MUL_FIXED(cx,sy);
/* m21 = cx*sz */
m1->mat21=MUL_FIXED(cx,sz);
/* m22 = cx*cz */
m1->mat22=MUL_FIXED(cx,cz);
/* m23 = -sx */
m1->mat23=-sx;
/* m31 = -sy*cz + sx*cy*sz */
m1->mat31=MUL_FIXED(-sy,cz);
t=MUL_FIXED(sx,cy);
t=MUL_FIXED(t,sz);
m1->mat31+=t;
/* m32 = sy*sz + sx*cy*cz */
m1->mat32=MUL_FIXED(sy,sz);
t=MUL_FIXED(sx,cy);
t=MUL_FIXED(t,cz);
m1->mat32+=t;
/* m33 = cx*cy */
m1->mat33=MUL_FIXED(cx,cy);
}
/*
Create a Unit Vector from three Euler Angles
*/
void CreateEulerVector(EULER *e, VECTORCH *v)
{
int t, sx, sy, sz, cx, cy, cz;
sx = GetSin(e->EulerX);
sy = GetSin(e->EulerY);
sz = GetSin(e->EulerZ);
cx = GetCos(e->EulerX);
cy = GetCos(e->EulerY);
cz = GetCos(e->EulerZ);
/* x = -sy*cz + sx*cy*sz */
v->vx = MUL_FIXED(-sy, cz);
t = MUL_FIXED(sx, cy);
t = MUL_FIXED(t, sz);
v->vx += t;
/* y = sy*sz + sx*cy*cz */
v->vy = MUL_FIXED(sy, sz);
t = MUL_FIXED(sx, cy);
t = MUL_FIXED(t, cz);
v->vy += t;
/* z = cx*cy */
v->vz = MUL_FIXED(cx,cy);
}
/*
Matrix Multiply Function
A 3x3 Matrix is represented here as
m11 m12 m13
m21 m22 m23
m31 m32 m33
Row #1 (r1) of the matrix is m11 m12 m13
Column #1 (c1) of the matrix is m11 m32 m31
Under multiplication
m'' = m x m'
where
m11'' = c1.r1'
m12'' = c2.r1'
m13'' = c3.r1'
m21'' = c1.r2'
m22'' = c2.r2'
m23'' = c3.r2'
m31'' = c1.r3'
m32'' = c2.r3'
m33'' = c3.r3'
*/
void MatrixMultiply(struct matrixch *m1, struct matrixch *m2, struct matrixch *m3)
{
MATRIXCH TmpMat;
/* m11'' = c1.r1' */
TmpMat.mat11=MUL_FIXED(m1->mat11,m2->mat11);
TmpMat.mat11+=MUL_FIXED(m1->mat21,m2->mat12);
TmpMat.mat11+=MUL_FIXED(m1->mat31,m2->mat13);
/* m12'' = c2.r1' */
TmpMat.mat12=MUL_FIXED(m1->mat12,m2->mat11);
TmpMat.mat12+=MUL_FIXED(m1->mat22,m2->mat12);
TmpMat.mat12+=MUL_FIXED(m1->mat32,m2->mat13);
/* m13'' = c3.r1' */
TmpMat.mat13=MUL_FIXED(m1->mat13,m2->mat11);
TmpMat.mat13+=MUL_FIXED(m1->mat23,m2->mat12);
TmpMat.mat13+=MUL_FIXED(m1->mat33,m2->mat13);
/* m21'' = c1.r2' */
TmpMat.mat21=MUL_FIXED(m1->mat11,m2->mat21);
TmpMat.mat21+=MUL_FIXED(m1->mat21,m2->mat22);
TmpMat.mat21+=MUL_FIXED(m1->mat31,m2->mat23);
/* m22'' = c2.r2' */
TmpMat.mat22=MUL_FIXED(m1->mat12,m2->mat21);
TmpMat.mat22+=MUL_FIXED(m1->mat22,m2->mat22);
TmpMat.mat22+=MUL_FIXED(m1->mat32,m2->mat23);
/* m23'' = c3.r2' */
TmpMat.mat23=MUL_FIXED(m1->mat13,m2->mat21);
TmpMat.mat23+=MUL_FIXED(m1->mat23,m2->mat22);
TmpMat.mat23+=MUL_FIXED(m1->mat33,m2->mat23);
/* m31'' = c1.r3' */
TmpMat.mat31=MUL_FIXED(m1->mat11,m2->mat31);
TmpMat.mat31+=MUL_FIXED(m1->mat21,m2->mat32);
TmpMat.mat31+=MUL_FIXED(m1->mat31,m2->mat33);
/* m32'' = c2.r3' */
TmpMat.mat32=MUL_FIXED(m1->mat12,m2->mat31);
TmpMat.mat32+=MUL_FIXED(m1->mat22,m2->mat32);
TmpMat.mat32+=MUL_FIXED(m1->mat32,m2->mat33);
/* m33'' = c3.r3' */
TmpMat.mat33=MUL_FIXED(m1->mat13,m2->mat31);
TmpMat.mat33+=MUL_FIXED(m1->mat23,m2->mat32);
TmpMat.mat33+=MUL_FIXED(m1->mat33,m2->mat33);
/* Finally, copy TmpMat to m3 */
CopyMatrix(&TmpMat, m3);
}
/*
Transpose Matrix
*/
void TransposeMatrixCH(MATRIXCH *m1)
{
int t;
t=m1->mat12;
m1->mat12=m1->mat21;
m1->mat21=t;
t=m1->mat13;
m1->mat13=m1->mat31;
m1->mat31=t;
t=m1->mat23;
m1->mat23=m1->mat32;
m1->mat32=t;
}
/*
Copy Vector
*/
void CopyVector(VECTORCH *v1, VECTORCH *v2)
{
/* Copy VECTORCH v1 -> VECTORCH v2 */
v2->vx=v1->vx;
v2->vy=v1->vy;
v2->vz=v1->vz;
}
/*
Copy Location
*/
void CopyLocation(VECTORCH *v1, VECTORCH *v2)
{
/* Copy VECTORCH v1 -> VECTORCH v2 */
v2->vx=v1->vx;
v2->vy=v1->vy;
v2->vz=v1->vz;
}
/*
Copy Euler
*/
void CopyEuler(EULER *e1, EULER *e2)
{
/* Copy EULER e1 -> EULER e2 */
e2->EulerX=e1->EulerX;
e2->EulerY=e1->EulerY;
e2->EulerZ=e1->EulerZ;
}
/*
Copy Matrix
*/
void CopyMatrix(MATRIXCH *m1, MATRIXCH *m2)
{
/* Copy MATRIXCH m1 -> MATRIXCH m2 */
m2->mat11=m1->mat11;
m2->mat12=m1->mat12;
m2->mat13=m1->mat13;
m2->mat21=m1->mat21;
m2->mat22=m1->mat22;
m2->mat23=m1->mat23;
m2->mat31=m1->mat31;
m2->mat32=m1->mat32;
m2->mat33=m1->mat33;
}
/*
Make a Vector.
v3 = v1 - v2
*/
void MakeVector(VECTORCH *v1, VECTORCH *v2, VECTORCH *v3)
{
v3->vx = v1->vx - v2->vx;
v3->vy = v1->vy - v2->vy;
v3->vz = v1->vz - v2->vz;
}
/*
Add a Vector.
v2 = v2 + v1
*/
void AddVector(VECTORCH *v1, VECTORCH *v2)
{
v2->vx += v1->vx;
v2->vy += v1->vy;
v2->vz += v1->vz;
}
/*
Subtract a Vector.
v2 = v2 - v1
*/
void SubVector(VECTORCH *v1, VECTORCH *v2)
{
v2->vx -= v1->vx;
v2->vy -= v1->vy;
v2->vz -= v1->vz;
}
/*
Matrix Rotatation of a Vector
Overwrite the Source Vector with the Rotated Vector
x' = v.c1
y' = v.c2
z' = v.c3
*/
void _RotateVector(VECTORCH *v, MATRIXCH* m)
{
int x, y, z;
x = MUL_FIXED(m->mat11, v->vx);
x += MUL_FIXED(m->mat21, v->vy);
x += MUL_FIXED(m->mat31, v->vz);
y = MUL_FIXED(m->mat12, v->vx);
y += MUL_FIXED(m->mat22, v->vy);
y += MUL_FIXED(m->mat32, v->vz);
z = MUL_FIXED(m->mat13, v->vx);
z += MUL_FIXED(m->mat23, v->vy);
z += MUL_FIXED(m->mat33, v->vz);
v->vx = x;
v->vy = y;
v->vz = z;
}
/*
Matrix Rotation of a Source Vector using a Matrix
Copying to a Destination Vector
x' = v.c1
y' = v.c2
z' = v.c3
*/
void _RotateAndCopyVector(VECTORCH *v1, VECTORCH *v2, MATRIXCH *m)
{
v2->vx=MUL_FIXED(m->mat11,v1->vx);
v2->vx+=MUL_FIXED(m->mat21,v1->vy);
v2->vx+=MUL_FIXED(m->mat31,v1->vz);
v2->vy=MUL_FIXED(m->mat12,v1->vx);
v2->vy+=MUL_FIXED(m->mat22,v1->vy);
v2->vy+=MUL_FIXED(m->mat32,v1->vz);
v2->vz=MUL_FIXED(m->mat13,v1->vx);
v2->vz+=MUL_FIXED(m->mat23,v1->vy);
v2->vz+=MUL_FIXED(m->mat33,v1->vz);
}
/*
Matrix to Euler Angles
Maths overflow is a real problem for this function. To prevent overflows
the matrix Sines and Cosines are calculated using values scaled down by 4.
sinx = -M23
cosx = sqr ( 1 - sinx^2 )
siny = M13 / cosx
cosy = M33 / cosx
sinz = M21 / cosx
cosz = M22 / cosx
*/
#define m2e_scale 2
#define ONE_FIXED_S ((ONE_FIXED >> m2e_scale) - 1)
#define m2e_shift 14
#define j_and_r_change Yes
void MatrixToEuler(MATRIXCH *m, EULER *e)
{
int x, sinx, cosx, siny, cosy, sinz, cosz;
int abs_cosx, abs_cosy, abs_cosz;
int SineMatrixPitch, SineMatrixYaw, SineMatrixRoll;
int CosMatrixPitch, CosMatrixYaw, CosMatrixRoll;
#if 0
textprint("CosMatrixPitch = %d\n", CosMatrixPitch);
/* WaitForReturn(); */
#endif
if(m->mat32 >-65500 && m->mat32<65500)
{
/* Yaw */
/* Pitch */
#if j_and_r_change
SineMatrixPitch = -m->mat32;
#else
SineMatrixPitch = -m->mat23;
#endif
SineMatrixPitch >>= m2e_scale;
#if 0
textprint("SineMatrixPitch = %d\n", SineMatrixPitch);
/* WaitForReturn(); */
#endif
CosMatrixPitch = SineMatrixPitch * SineMatrixPitch;
CosMatrixPitch >>= m2e_shift;
CosMatrixPitch = -CosMatrixPitch;
CosMatrixPitch += ONE_FIXED_S;
CosMatrixPitch *= ONE_FIXED_S;
CosMatrixPitch = SqRoot32(CosMatrixPitch);
if(CosMatrixPitch) {
if(CosMatrixPitch > ONE_FIXED_S) CosMatrixPitch = ONE_FIXED_S;
else if(CosMatrixPitch < -ONE_FIXED_S) CosMatrixPitch = -ONE_FIXED_S;
}
else CosMatrixPitch = 1;
SineMatrixYaw = WideMulNarrowDiv(
#if j_and_r_change
m->mat31 >> m2e_scale, ONE_FIXED_S, CosMatrixPitch);
#else
m->mat13 >> m2e_scale, ONE_FIXED_S, CosMatrixPitch);
#endif
#if 0
textprint("SineMatrixYaw = %d\n", SineMatrixYaw);
/* WaitForReturn(); */
#endif
CosMatrixYaw = WideMulNarrowDiv(
m->mat33 >> m2e_scale, ONE_FIXED_S, CosMatrixPitch);
#if 0
textprint("CosMatrixYaw = %d\n", CosMatrixYaw);
/* WaitForReturn(); */
#endif
/* Roll */
SineMatrixRoll = WideMulNarrowDiv(
#if j_and_r_change
m->mat12 >> m2e_scale, ONE_FIXED_S, CosMatrixPitch);
#else
m->mat21 >> m2e_scale, ONE_FIXED_S, CosMatrixPitch);
#endif
#if 0
textprint("SineMatrixRoll = %d\n", SineMatrixRoll);
/* WaitForReturn(); */
#endif
CosMatrixRoll = WideMulNarrowDiv(
m->mat22 >> m2e_scale, ONE_FIXED_S, CosMatrixPitch);
#if 0
textprint("CosMatrixRoll = %d\n", CosMatrixRoll);
/* WaitForReturn(); */
#endif
/* Tables are for values +- 2^16 */
sinx = SineMatrixPitch << m2e_scale;
siny = SineMatrixYaw << m2e_scale;
sinz = SineMatrixRoll << m2e_scale;
cosx = CosMatrixPitch << m2e_scale;
cosy = CosMatrixYaw << m2e_scale;
cosz = CosMatrixRoll << m2e_scale;
#if 0
textprint("sines = %d, %d, %d\n", sinx, siny, sinz);
textprint("cos's = %d, %d, %d\n", cosx, cosy, cosz);
/* WaitForReturn(); */
#endif
/* Absolute Cosines */
abs_cosx = cosx;
if(abs_cosx < 0) abs_cosx = -abs_cosx;
abs_cosy = cosy;
if(abs_cosy < 0) abs_cosy = -abs_cosy;
abs_cosz = cosz;
if(abs_cosz < 0) abs_cosz = -abs_cosz;
/* Euler X */
if(abs_cosx > Cosine45) {
x = ArcSin(sinx);
if(cosx < 0) {
x = -x;
x += deg180;
x &= wrap360;
}
}
else {
x = ArcCos(cosx);
if(sinx < 0) {
x = -x;
x &= wrap360;
}
}
#if (j_and_r_change == No)
x = -x;
x &= wrap360;
#endif
e->EulerX = x;
/* Euler Y */
if(abs_cosy > Cosine45) {
x = ArcSin(siny);
if(cosy < 0) {
x = -x;
x += deg180;
x &= wrap360;
}
}