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TempleOS-Rijn/LT/Adam/Gr/GrMath.APZ
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Terry A. Davis 0e9364ff4c LTCD_070816.ISO
2018-09-08 21:45:20 +02:00

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#help_index "Graphics/Math"
I8 GrXOffsets[8]={-1,0,1,-1,1,-1,0,1},
GrYOffsets[8]={-1,-1,-1,0,0,1,1,1};
public void Line(void *aux_data,
I8 x1,I8 y1,I8 z1,
I8 x2,I8 y2,I8 z2,
void plot_cb(void *aux,I8 x,I8 y,I8 z),
I8 step=1,I8 start=0)
{
I8 i,j,d,dx=x2-x1,dy=y2-y1,dz=z2-z1;
I8 adx=AbsI8(dx),ady=AbsI8(dy),adz=AbsI8(dz);
if (adx>=ady) {
if (adx>=adz) {
if (d=adx) {
if (dx>=0)
dx=0x100000000;
else
dx=-0x100000000;
dy=dy<<32/d;
dz=dz<<32/d;
}
} else {
if (d=adz) {
dx=dx<<32/d;
dy=dy<<32/d;
if (dz>=0)
dz=0x100000000;
else
dz=-0x100000000;
}
}
} else {
if (ady>=adz) {
if (d=ady) {
dx=dx<<32/d;
if (dy>=0)
dy=0x100000000;
else
dy=-0x100000000;
dz=dz<<32/d;
}
} else {
if (d=adz) {
dx=dx<<32/d;
dy=dy<<32/d;
if (dz>=0)
dz=0x100000000;
else
dz=-0x100000000;
}
}
}
x1<<=32; y1<<=32; z1<<=32;
for (j=0;j<start;j++) {
x1+=dx; y1+=dy; z1+=dz;
}
if (step==1) {
for (i=start;i<=d;i++) {
plot_cb(aux_data,x1.i4[1],y1.i4[1],z1.i4[1]);
x1+=dx; y1+=dy; z1+=dz;
}
} else {
for (i=start;i<=d;i+=step) {
plot_cb(aux_data,x1.i4[1],y1.i4[1],z1.i4[1]);
for (j=0;j<step;j++) {
x1+=dx; y1+=dy; z1+=dz;
}
}
}
}
public void Box(void *aux_data,
I8 x1,I8 y1,I8 z1,
I8 x2,I8 y2,I8 z2,
I8 x3,I8 y3,I8 z3,
void plot_cb(void *aux,I8 x,I8 y,I8 z))
{
I8 i,j,
d1,dx1=x2-x1,dy1=y2-y1,dz1=z2-z1,
d2,dx2=x3-x1,dy2=y3-y1,dz2=z3-z1,
adx1=AbsI8(dx1),ady1=AbsI8(dy1),adz1=AbsI8(dz1),
adx2=AbsI8(dx2),ady2=AbsI8(dy2),adz2=AbsI8(dz2);
if (adx1>=ady1)
d1=(adx1>=adz1) ? adx1:adz1;
else
d1=(ady1>=adz1) ? ady1:adz1;
d1<<=1;
if (d1) {
dx1=dx1<<32/d1;
dy1=dy1<<32/d1;
dz1=dz1<<32/d1;
}
if (adx2>=ady2)
d2=(adx2>=adz2) ? adx2:adz2;
else
d2=(ady2>=adz2) ? ady2:adz2;
d2<<=1;
if (d2) {
dx2=dx2<<32/d2;
dy2=dy2<<32/d2;
dz2=dz2<<32/d2;
}
x1<<=32; y1<<=32; z1<<=32;
for (j=0;j<=d1;j++) {
x2=x1; y2=y1; z2=z1;
for (i=0;i<=d2;i++) {
plot_cb(aux_data,x2.i4[1],y2.i4[1],z2.i4[1]);
x2+=dx2; y2+=dy2; z2+=dz2;
}
x1+=dx1; y1+=dy1; z1+=dz1;
}
}
#help_index "Graphics/Math/3D Transformation"
I8 gr_scale;
gr_scale.u4[0]=0;
gr_scale.u4[1]=1;
void *gr_screen_capture=NULL;
public void GrRotate(I8 *r,I8 *x,I8 *y,I8 *z)
{
I8 x1,y1,z1,xx=*x,yy=*y,zz=*z;
x1=(r[0]*xx+r[1]*yy+r[2]*zz+r[3])>>32;
y1=(r[4]*xx+r[5]*yy+r[6]*zz+r[7])>>32;
z1=(r[8]*xx+r[9]*yy+r[10]*zz+r[11])>>32;
*x=x1;*y=y1;*z=z1;
}
public void GrTransform(GrBitMap *base,I8 *x,I8 *y,I8 *z)
{
GrRotate(base->r,x,y,z);
*x+=base->x;
*y+=base->y;
*z+=base->z;
}
public I8 *GrTheta(double theta,TssStruct *tss=NULL)
{
double my_cos,my_sin;
I8 *r=MAllocZ(sizeof(I8)*16,tss);
my_cos=Cos(theta)*gr_scale;
my_sin=Sin(theta)*gr_scale;
r[0]=my_cos;
r[5]=my_cos;
r[4]=my_sin;
r[1]=-my_sin;
r[10]=gr_scale;
return r;
}
public I8 *GrPhi(double phi,TssStruct *tss=NULL)
{
double my_cos,my_sin;
I8 *r=MAllocZ(sizeof(I8)*16,tss);
my_cos=Cos(phi)*gr_scale;
my_sin=Sin(phi)*gr_scale;
r[5]=my_cos;
r[10]=my_cos;
r[9]=my_sin;
r[6]=-my_sin;
r[0]=gr_scale;
return r;
}
public I8 *GrScaleMat(I8 *m1,double s,TssStruct *tss=NULL)
{
I8 i,*r=MAllocZ(sizeof(I8)*16,tss);
for (i=0;i<16;i++)
r[i]=m1[i]*s;
return r;
}
public I8 *GrMulMat(I8 *m1,I8 *m2,TssStruct *tss=NULL)
{
I8 *r=MAllocZ(sizeof(I8)*16,tss);
I8 i,j,k;
double d;
for (i=0;i<4;i++) {
for (j=0;j<4;j++) {
for (k=0;k<4;k++) {
d=m1[k+4*j];
d*=m2[i+4*k];
d/=gr_scale;
r[i+4*j]+=d;
}
}
}
return r;
}
public I8 GrDetMat(I8 *m1)
{
I8 i;
double m[16],d;
for (i=0;i<16;i++)
m[i]=m1[i]/(1.0*0x100000000);
d=m[0]*(m[5]*m[10]-m[6]*m[9])-
m[1]*(m[4]*m[10]-m[6]*m[8])+
m[2]*(m[4]*m[9]-m[5]*m[8]);
return d*0x100000000;
}
public void GrScalePenWidth(GrBitMap *base)
{
I8 d;
if (base->flags&BMF_TRANSFORMATION) {
if (base->pen_width) {
d=base->pen_width*GrDetMat(base->r)+0x80000000;
base->pen_width=d.u4[1];
if (base->pen_width<1)
base->pen_width=1;
}
}
}
public void GrSetIdent(I8 *r)
{
MemSet(r,0,16<<3);
r[0].u4[1]=1;
r[5].u4[1]=1;
r[10].u4[1]=1;
r[15].u4[1]=1;
}
public void GrSetTranslation(I8 *r,I8 x,I8 y,I8 z)
{
r[3]=x<<32;
r[7]=y<<32;
r[11]=z<<32;
}
#help_index "Graphics/Math"
public void Circle(void *aux_data,
I8 cx,I8 cy,I8 cz,
I8 radius,
void plot_cb(void *aux,I8 x,I8 y,I8 z),
I8 step=1,
double start_rad=0,
double len_rad=pi2)
{
I8 i,j,len=len_rad*radius;
I8 x,y,x1,y1,s1,s2,c;
double t;
if (radius<0) return;
if (!radius) {
plot_cb(aux_data,cx,cy,cz);
return;
}
t=1.0/radius;
s1=(1<<24)*Sin(t);
s2=-s1;
c=(1<<24)*Cos(t);
if (start_rad) {
x=radius*Cos(start_rad);
y=-radius*Sin(start_rad);
} else {
x=radius;
y=0;
}
x<<=8;
y<<=8;
for (i=0;i<=len;i+=step) {
plot_cb(aux_data,cx+x>>8,cy+y>>8,cz);
for (j=0;j<step;j++) {
x1=(c*x+s1*y)>>24;
y1=(s2*x+c*y)>>24;
x=x1; y=y1;
}
}
}
public void Ellipse(void *aux_data,
I8 cx,I8 cy,I8 cz,
I8 x_radius,I8 y_radius,
void plot_cb(void *aux,I8 x,I8 y,I8 z),
double rot_angle=0,
I8 step=1,
double start_rad=0,
double len_rad=pi2)
{
I8 i,j,len;
I8 x,y,x1,y1,x2,y2, s1,s2,c, s12,s22,c2;
double t;
if (x_radius<0 || y_radius<0 || step<1)
return;
if (!x_radius && !y_radius) {
plot_cb(aux_data,cx,cy,cz);
return;
}
if (x_radius>=y_radius) {
t=1.0/x_radius;
len=len_rad*x_radius;
} else {
t=1.0/y_radius;
len=len_rad*y_radius;
}
s1=(1<<24)*Sin(t);
s2=-s1;
c=(1<<24)*Cos(t);
s12=(1<<24)*Sin(rot_angle);
s22=-s12;
c2=(1<<24)*Cos(rot_angle);
if (start_rad) {
x=x_radius*Cos(start_rad);
y=-x_radius*Sin(start_rad);
} else {
x=x_radius;
y=0;
}
x<<=8;
y<<=8;
x2=x;
y2=y;
y1=y2*y_radius/x_radius;
x=(c2*x2+s12*y1)>>24;
y=(s22*x2+c2*y1)>>24;
for (i=0;i<=len;i+=step) {
plot_cb(aux_data,cx+x>>8,cy+y>>8,cz);
for (j=0;j<step;j++) {
x1=(c*x2+s1*y2)>>24;
y1=(s2*x2+c*y2)>>24;
x2=x1;
y2=y1;
y1=y1*y_radius/x_radius;
x=(c2*x1+s12*y1)>>24;
y=(s22*x1+c2*y1)>>24;
}
}
}
public I8 DistP3I4(P3I4 *p1,P3I4 *p2)
{
return Sqrt(SqrI8(p1->x-p2->x)+SqrI8(p1->y-p2->y)+SqrI8(p1->z-p2->z));
}
public void Bezier2(void *aux_data,P3I4 *ctrl,void plot_cb(void *aux,I8 x,I8 y,I8 z))
{//2nd order
I8 x,y,z,xx,yy,zz,dx,dy,dz,d_max;
double x0=ctrl[0].x,y0=ctrl[0].y,z0=ctrl[0].z;
double x1=ctrl[1].x-x0,y1=ctrl[1].y-y0,z1=ctrl[1].z-z0;
double x2=ctrl[2].x-x0,y2=ctrl[2].y-y0,z2=ctrl[2].z-z0;
double t,d=DistP3I4(&ctrl[0],&ctrl[1])+
DistP3I4(&ctrl[1],&ctrl[2])+
DistP3I4(&ctrl[2],&ctrl[0]),
s=0.5/d,t1,t2;
xx=x0; yy=y0; zz=z0;
for (t=0.0;t<=1.0;t+=s) {
t1=t*(1.0-t);
t2=t*t;
x=x0+x1*t1+x2*t2;
y=y0+y1*t1+y2*t2;
z=z0+z1*t1+z2*t2;
dx=AbsI8(x-xx);
dy=AbsI8(y-yy);
dz=AbsI8(z-zz);
if (dx>dy)
d_max=dx;
else
d_max=dy;
if (dz>d_max)
d_max=dz;
if (!d_max)
s*=1.1;
else {
s*=0.9;
plot_cb(aux_data,x,y,z);
xx=x;yy=y;zz=z;
}
}
}
public void Bezier3(void *aux_data,P3I4 *ctrl,void plot_cb(void *aux,I8 x,I8 y,I8 z))
{ //3rd order
I8 x,y,z,xx,yy,zz,dx,dy,dz,d_max;
double x0=ctrl[0].x,y0=ctrl[0].y,z0=ctrl[0].z;
double x1=ctrl[1].x-x0,y1=ctrl[1].y-y0,z1=ctrl[1].z-z0;
double x2=ctrl[2].x-x0,y2=ctrl[2].y-y0,z2=ctrl[2].z-z0;
double x3=ctrl[3].x-x0,y3=ctrl[3].y-y0,z3=ctrl[3].z-z0;
double t,d=DistP3I4(&ctrl[0],&ctrl[1])+
DistP3I4(&ctrl[1],&ctrl[2])+
DistP3I4(&ctrl[2],&ctrl[3])+
DistP3I4(&ctrl[3],&ctrl[0]),
s=0.5/d,nt,t1,t2,t3;
xx=x0; yy=y0; zz=z0;
for (t=0.0;t<=1.0;t+=s) {
nt=1.0-t;
t1=t*nt*nt;
t2=t*t*nt;
t3=t*t*t;
x=x0+x1*t1+x2*t2+x3*t3;
y=y0+y1*t1+y2*t2+y3*t3;
z=z0+z1*t1+z2*t2+z3*t3;
dx=AbsI8(x-xx);
dy=AbsI8(y-yy);
dz=AbsI8(z-zz);
if (dx>dy)
d_max=dx;
else
d_max=dy;
if (dz>d_max)
d_max=dz;
if (!d_max)
s*=1.1;
else {
s*=0.9;
plot_cb(aux_data,x,y,z);
xx=x;yy=y;zz=z;
}
}
}
public void BSpline2(void *aux_data,P3I4 *ctrl,I8 cnt,void plot_cb(void *aux,I8 x,I8 y,I8 z),BoolU4 closed=FALSE)
{ //2nd order
I8 i,j;
P3I4 *c;
if (cnt<3) return;
if (closed) {
cnt++;
c=MAlloc(sizeof(P3I4)*(cnt*2-1));
j=1;
for (i=0;i<cnt-2;i++) {
c[j].x=(ctrl[i].x+ctrl[i+1].x)/2.0;
c[j].y=(ctrl[i].y+ctrl[i+1].y)/2.0;
c[j].z=(ctrl[i].z+ctrl[i+1].z)/2.0;
j+=2;
}
c[j].x=(ctrl[0].x+ctrl[cnt-2].x)/2.0;
c[j].y=(ctrl[0].y+ctrl[cnt-2].y)/2.0;
c[j].z=(ctrl[0].z+ctrl[cnt-2].z)/2.0;
c[0].x=(c[1].x+c[j].x)/2.0;
c[0].y=(c[1].y+c[j].y)/2.0;
c[0].z=(c[1].z+c[j].z)/2.0;
j=2;
for (i=0;i<cnt-2;i++) {
c[j].x=(c[j-1].x+c[j+1].x)/2.0;
c[j].y=(c[j-1].y+c[j+1].y)/2.0;
c[j].z=(c[j-1].z+c[j+1].z)/2.0;
j+=2;
}
c[j].x=c[0].x;
c[j].y=c[0].y;
c[j].z=c[0].z;
} else {
c=MAlloc(sizeof(P3I4)*(cnt*2-1));
c[0].x=ctrl[0].x;
c[0].y=ctrl[0].y;
c[0].z=ctrl[0].z;
c[cnt*2-2].x=ctrl[cnt-1].x;
c[cnt*2-2].y=ctrl[cnt-1].y;
c[cnt*2-2].z=ctrl[cnt-1].z;
j=1;
for (i=0;i<cnt-1;i++) {
c[j].x=(ctrl[i].x+ctrl[i+1].x)/2.0;
c[j].y=(ctrl[i].y+ctrl[i+1].y)/2.0;
c[j].z=(ctrl[i].z+ctrl[i+1].z)/2.0;
j+=2;
}
j=2;
for (i=0;i<cnt-2;i++) {
c[j].x=(c[j-1].x+c[j+1].x)/2.0;
c[j].y=(c[j-1].y+c[j+1].y)/2.0;
c[j].z=(c[j-1].z+c[j+1].z)/2.0;
j+=2;
}
}
for (i=0;i<cnt*2-2;i+=2)
Bezier2(aux_data,&c[i],plot_cb);
Free(c);
}
public void BSpline3(void *aux_data,P3I4 *ctrl,I8 cnt,void plot_cb(void *aux,I8 x,I8 y,I8 z),BoolU4 closed=FALSE)
{ //3rd order
I8 i,j;
double x,y,z;
P3I4 *c;
if (cnt<3) return;
if (closed) {
cnt++;
c=MAlloc(sizeof(P3I4)*(cnt*3-2));
j=1;
for (i=0;i<cnt-2;i++) {
x=ctrl[i].x;
y=ctrl[i].y;
z=ctrl[i].z;
c[j].x=(ctrl[i+1].x-x)/3.0+x;
c[j].y=(ctrl[i+1].y-y)/3.0+y;
c[j].z=(ctrl[i+1].z-z)/3.0+z;
j++;
c[j].x=2.0*(ctrl[i+1].x-x)/3.0+x;
c[j].y=2.0*(ctrl[i+1].y-y)/3.0+y;
c[j].z=2.0*(ctrl[i+1].z-z)/3.0+z;
j+=2;
}
x=ctrl[cnt-2].x;
y=ctrl[cnt-2].y;
z=ctrl[cnt-2].z;
c[j].x=(ctrl[0].x-x)/3.0+x;
c[j].y=(ctrl[0].y-y)/3.0+y;
c[j].z=(ctrl[0].z-z)/3.0+z;
j++;
c[j].x=2.0*(ctrl[0].x-x)/3.0+x;
c[j].y=2.0*(ctrl[0].y-y)/3.0+y;
c[j].z=2.0*(ctrl[0].z-z)/3.0+z;
c[0].x=(c[1].x+c[j].x)/2.0;
c[0].y=(c[1].y+c[j].y)/2.0;
c[0].z=(c[1].z+c[j].z)/2.0;
j=3;
for (i=0;i<cnt-2;i++) {
c[j].x=(c[j-1].x+c[j+1].x)/2.0;
c[j].y=(c[j-1].y+c[j+1].y)/2.0;
c[j].z=(c[j-1].z+c[j+1].z)/2.0;
j+=3;
}
c[j].x=c[0].x;
c[j].y=c[0].y;
c[j].z=c[0].z;
} else {
c=MAlloc(sizeof(P3I4)*(cnt*3-2));
c[0].x=ctrl[0].x;
c[0].y=ctrl[0].y;
c[0].z=ctrl[0].z;
c[cnt*3-3].x=ctrl[cnt-1].x;
c[cnt*3-3].y=ctrl[cnt-1].y;
c[cnt*3-3].z=ctrl[cnt-1].z;
j=1;
for (i=0;i<cnt-1;i++) {
x=ctrl[i].x;
y=ctrl[i].y;
z=ctrl[i].z;
c[j].x=(ctrl[i+1].x-x)/3.0+x;
c[j].y=(ctrl[i+1].y-y)/3.0+y;
c[j].z=(ctrl[i+1].z-z)/3.0+z;
j++;
c[j].x=2.0*(ctrl[i+1].x-x)/3.0+x;
c[j].y=2.0*(ctrl[i+1].y-y)/3.0+y;
c[j].z=2.0*(ctrl[i+1].z-z)/3.0+z;
j+=2;
}
j=3;
for (i=0;i<cnt-2;i++) {
c[j].x=(c[j-1].x+c[j+1].x)/2.0;
c[j].y=(c[j-1].y+c[j+1].y)/2.0;
c[j].z=(c[j-1].z+c[j+1].z)/2.0;
j+=3;
}
}
for (i=0;i<cnt*3-3;i+=3)
Bezier3(aux_data,&c[i],plot_cb);
Free(c);
}
#help_index "Graphics"
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