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- /*% cc -gpc %
- * These transformation routines maintain stacks of transformations
- * and their inverses.
- * t=pushmat(t) push matrix stack
- * t=popmat(t) pop matrix stack
- * rot(t, a, axis) multiply stack top by rotation
- * qrot(t, q) multiply stack top by rotation, q is unit quaternion
- * scale(t, x, y, z) multiply stack top by scale
- * move(t, x, y, z) multiply stack top by translation
- * xform(t, m) multiply stack top by m
- * ixform(t, m, inv) multiply stack top by m. inv is the inverse of m.
- * look(t, e, l, u) multiply stack top by viewing transformation
- * persp(t, fov, n, f) multiply stack top by perspective transformation
- * viewport(t, r, aspect)
- * multiply stack top by window->viewport transformation.
- */
- #include <u.h>
- #include <libc.h>
- #include <draw.h>
- #include <geometry.h>
- Space *pushmat(Space *t){
- Space *v;
- v=malloc(sizeof(Space));
- if(t==0){
- ident(v->t);
- ident(v->tinv);
- }
- else
- *v=*t;
- v->next=t;
- return v;
- }
- Space *popmat(Space *t){
- Space *v;
- if(t==0) return 0;
- v=t->next;
- free(t);
- return v;
- }
- void rot(Space *t, double theta, int axis){
- double s=sin(radians(theta)), c=cos(radians(theta));
- Matrix m, inv;
- register i=(axis+1)%3, j=(axis+2)%3;
- ident(m);
- m[i][i] = c;
- m[i][j] = -s;
- m[j][i] = s;
- m[j][j] = c;
- ident(inv);
- inv[i][i] = c;
- inv[i][j] = s;
- inv[j][i] = -s;
- inv[j][j] = c;
- ixform(t, m, inv);
- }
- void qrot(Space *t, Quaternion q){
- Matrix m, inv;
- int i, j;
- qtom(m, q);
- for(i=0;i!=4;i++) for(j=0;j!=4;j++) inv[i][j]=m[j][i];
- ixform(t, m, inv);
- }
- void scale(Space *t, double x, double y, double z){
- Matrix m, inv;
- ident(m);
- m[0][0]=x;
- m[1][1]=y;
- m[2][2]=z;
- ident(inv);
- inv[0][0]=1/x;
- inv[1][1]=1/y;
- inv[2][2]=1/z;
- ixform(t, m, inv);
- }
- void move(Space *t, double x, double y, double z){
- Matrix m, inv;
- ident(m);
- m[0][3]=x;
- m[1][3]=y;
- m[2][3]=z;
- ident(inv);
- inv[0][3]=-x;
- inv[1][3]=-y;
- inv[2][3]=-z;
- ixform(t, m, inv);
- }
- void xform(Space *t, Matrix m){
- Matrix inv;
- if(invertmat(m, inv)==0) return;
- ixform(t, m, inv);
- }
- void ixform(Space *t, Matrix m, Matrix inv){
- matmul(t->t, m);
- matmulr(t->tinv, inv);
- }
- /*
- * multiply the top of the matrix stack by a view-pointing transformation
- * with the eyepoint at e, looking at point l, with u at the top of the screen.
- * The coordinate system is deemed to be right-handed.
- * The generated transformation transforms this view into a view from
- * the origin, looking in the positive y direction, with the z axis pointing up,
- * and x to the right.
- */
- void look(Space *t, Point3 e, Point3 l, Point3 u){
- Matrix m, inv;
- Point3 r;
- l=unit3(sub3(l, e));
- u=unit3(vrem3(sub3(u, e), l));
- r=cross3(l, u);
- /* make the matrix to transform from (rlu) space to (xyz) space */
- ident(m);
- m[0][0]=r.x; m[0][1]=r.y; m[0][2]=r.z;
- m[1][0]=l.x; m[1][1]=l.y; m[1][2]=l.z;
- m[2][0]=u.x; m[2][1]=u.y; m[2][2]=u.z;
- ident(inv);
- inv[0][0]=r.x; inv[0][1]=l.x; inv[0][2]=u.x;
- inv[1][0]=r.y; inv[1][1]=l.y; inv[1][2]=u.y;
- inv[2][0]=r.z; inv[2][1]=l.z; inv[2][2]=u.z;
- ixform(t, m, inv);
- move(t, -e.x, -e.y, -e.z);
- }
- /*
- * generate a transformation that maps the frustum with apex at the origin,
- * apex angle=fov and clipping planes y=n and y=f into the double-unit cube.
- * plane y=n maps to y'=-1, y=f maps to y'=1
- */
- int persp(Space *t, double fov, double n, double f){
- Matrix m;
- double z;
- if(n<=0 || f<=n || fov<=0 || 180<=fov) /* really need f!=n && sin(v)!=0 */
- return -1;
- z=1/tan(radians(fov)/2);
- m[0][0]=z; m[0][1]=0; m[0][2]=0; m[0][3]=0;
- m[1][0]=0; m[1][1]=(f+n)/(f-n); m[1][2]=0; m[1][3]=f*(1-m[1][1]);
- m[2][0]=0; m[2][1]=0; m[2][2]=z; m[2][3]=0;
- m[3][0]=0; m[3][1]=1; m[3][2]=0; m[3][3]=0;
- xform(t, m);
- return 0;
- }
- /*
- * Map the unit-cube window into the given screen viewport.
- * r has min at the top left, max just outside the lower right. Aspect is the
- * aspect ratio (dx/dy) of the viewport's pixels (not of the whole viewport!)
- * The whole window is transformed to fit centered inside the viewport with equal
- * slop on either top and bottom or left and right, depending on the viewport's
- * aspect ratio.
- * The window is viewed down the y axis, with x to the left and z up. The viewport
- * has x increasing to the right and y increasing down. The window's y coordinates
- * are mapped, unchanged, into the viewport's z coordinates.
- */
- void viewport(Space *t, Rectangle r, double aspect){
- Matrix m;
- double xc, yc, wid, hgt, scale;
- xc=.5*(r.min.x+r.max.x);
- yc=.5*(r.min.y+r.max.y);
- wid=(r.max.x-r.min.x)*aspect;
- hgt=r.max.y-r.min.y;
- scale=.5*(wid<hgt?wid:hgt);
- ident(m);
- m[0][0]=scale;
- m[0][3]=xc;
- m[1][1]=0;
- m[1][2]=-scale;
- m[1][3]=yc;
- m[2][1]=1;
- m[2][2]=0;
- /* should get inverse by hand */
- xform(t, m);
- }
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