diff options
author | rodri <rgl@antares-labs.eu> | 2023-01-28 22:16:25 +0000 |
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committer | rodri <rgl@antares-labs.eu> | 2023-01-28 22:16:25 +0000 |
commit | 983fae140a1e162d947eab8b8a0d9acba291d3a8 (patch) | |
tree | ef7a0de9a51ebbfd086e9293d2a22e1da387ee2d | |
download | threedee-983fae140a1e162d947eab8b8a0d9acba291d3a8.tar.gz threedee-983fae140a1e162d947eab8b8a0d9acba291d3a8.tar.bz2 threedee-983fae140a1e162d947eab8b8a0d9acba291d3a8.zip |
-rw-r--r-- | brick.pic | bin | 0 -> 266 bytes | |||
-rw-r--r-- | dat.h | 37 | ||||
-rw-r--r-- | fns.h | 31 | ||||
-rw-r--r-- | main.c | 339 | ||||
-rw-r--r-- | matrix.c | 82 | ||||
-rw-r--r-- | mdl/box.obj | 30 | ||||
-rw-r--r-- | mdl/rocket.obj | 143 | ||||
-rw-r--r-- | mdl/sphere.obj | 1463 | ||||
-rw-r--r-- | mdl/sphere16.obj | 13127 | ||||
-rw-r--r-- | mdl/sphere32.obj | 23333 | ||||
-rw-r--r-- | mkfile | 16 | ||||
-rw-r--r-- | obj.c | 65 | ||||
-rw-r--r-- | readme.md | 4 | ||||
-rw-r--r-- | triangle.c | 58 | ||||
-rw-r--r-- | util.c | 29 | ||||
-rw-r--r-- | vector.c | 60 | ||||
-rw-r--r-- | vector3.c | 59 |
17 files changed, 38876 insertions, 0 deletions
diff --git a/brick.pic b/brick.pic Binary files differnew file mode 100644 index 0000000..979c7d1 --- /dev/null +++ b/brick.pic @@ -0,0 +1,37 @@ +#define DEG 0.01745329251994330 + +enum { + STACK = 8192, + SEC = 1000, + FPS = 60, + FOV = 90 +}; + +typedef struct Vector Vector; +typedef struct Vector3 Vector3; +typedef double Matrix[4][4]; +typedef struct Triangle Triangle; +typedef struct Triangle3 Triangle3; +typedef struct Mesh Mesh; + +struct Vector { + double x, y; +}; + +struct Vector3 { + double x, y, z; +}; + +struct Triangle { + Point p0, p1, p2; +}; + +struct Triangle3 { + Vector3 p0, p1, p2; + Image *tx; +}; + +struct Mesh { + Triangle3 *tris; + int ntri; +}; @@ -0,0 +1,31 @@ +int objread(char *, Triangle3 **); +Triangle Trian(int, int, int, int, int, int); +Triangle Trianpt(Point, Point, Point); +Point centroid(Triangle); +void triangle(Image *, Triangle, int, Image *, Point); +void filltriangle(Image *, Triangle, Image *, Point); +Triangle rotatriangle(Triangle, double, Point); +Vector Vec(double, double); +Vector addvec(Vector, Vector); +Vector subvec(Vector, Vector); +Vector mulvec(Vector, double); +double dotvec(Vector, Vector); +Vector normvec(Vector); +Vector3 Vec3(double, double, double); +Vector3 addvec3(Vector3, Vector3); +Vector3 subvec3(Vector3, Vector3); +Vector3 mulvec3(Vector3, double); +double dotvec3(Vector3, Vector3); +Vector3 crossvec(Vector3, Vector3); +Vector3 normvec3(Vector3); +void addm(Matrix, Matrix); +void subm(Matrix, Matrix); +void mulm(Matrix, Matrix); +void transm(Matrix); +double detm(Matrix); +Vector3 mulvecm(Vector3, Matrix); +double round(double); +Point rotatept(Point, double, Point); +double hypot3(double, double, double); +void *emalloc(ulong); +void *erealloc(void *, ulong); @@ -0,0 +1,339 @@ +#include <u.h> +#include <libc.h> +#include <thread.h> +#include <draw.h> +#include <mouse.h> +#include <keyboard.h> +#include "dat.h" +#include "fns.h" + +Mousectl *mctl; +Keyboardctl *kctl; +Point orig; +Vector basis; +double Znear, Zfar, Zoff, a; +Matrix proj; +Vector3 light; +double θ, ω; +double t0, Δt; +int dowireframe; +RWLock worldlock; + +Mesh model; +/*Triangle3 cube[] = { + 0,0,0, 0,1,0, 1,1,0, + 0,0,0, 1,1,0, 1,0,0, + + 1,0,0, 1,1,0, 1,1,1, + 1,0,0, 1,1,1, 1,0,1, + + 1,0,1, 1,1,1, 0,1,1, + 1,0,1, 0,1,1, 0,0,1, + + 0,0,1, 0,1,1, 0,1,0, + 0,0,1, 0,1,0, 0,0,0, + + 0,1,0, 0,1,1, 1,1,1, + 0,1,0, 1,1,1, 1,1,0, + + 1,0,1, 0,0,1, 0,0,0, + 1,0,1, 0,0,0, 1,0,0, +};*/ + +void * +emalloc(ulong n) +{ + void *p; + + p = malloc(n); + if(p == nil) + sysfatal("malloc: %r"); + memset(p, 0, n); + setmalloctag(p, getcallerpc(&n)); + return p; +} + +void * +erealloc(void *ptr, ulong n) +{ + void *p; + + p = realloc(ptr, n); + if(p == nil) + sysfatal("realloc: %r"); + setrealloctag(p, getcallerpc(&ptr)); + return p; +} + +Image * +eallocimage(Display *d, Rectangle r, ulong chan, int repl, ulong col) +{ + Image *i; + + i = allocimage(d, r, chan, repl, col); + if(i == nil) + sysfatal("allocimage: %r"); + return i; +} + +#pragma varargck type "V" Vector3 +int +Vfmt(Fmt *f) +{ + Vector3 v; + + v = va_arg(f->args, Vector3); + return fmtprint(f, "(%g %g %g)", v.x, v.y, v.z); +} + +#pragma varargck type "T" Triangle3 +int +Tfmt(Fmt *f) +{ + Triangle3 t; + + t = va_arg(f->args, Triangle3); + return fmtprint(f, "%V%V%V", t.p0, t.p1, t.p2); +} + +Point +vectopt(Vector v) +{ + return Pt(v.x, v.y); +} + +Point +toscreen(Vector p) +{ + return addpt(orig, Pt(p.x*basis.x, p.y*basis.y)); +} + +int +depthcmp(void *a, void *b) +{ + Triangle3 *ta, *tb; + double za, zb; + + ta = (Triangle3 *)a; + tb = (Triangle3 *)b; + za = (ta->p0.z + ta->p1.z + ta->p2.z)/3; + zb = (tb->p0.z + tb->p1.z + tb->p2.z)/3; + return za > zb ? -1 : 1; +} + +void +redraw(void) +{ + Triangle3 trans, *vistris; + Vector3 n; + Matrix Xrot = { + 1, 0, 0, 0, + 0, cos(θ/2), -sin(θ/2), 0, + 0, sin(θ/2), cos(θ/2), 0, + 0, 0, 0, 1, + }, Yrot = { + cos(θ/3), 0, -sin(θ/3), 0, + 0, 1, 0, 0, + sin(θ/3), 0, cos(θ/3), 0, + 0, 0, 0, 1, + }, Zrot = { + cos(θ), -sin(θ), 0, 0, + sin(θ), cos(θ), 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1, + }, RT = { + 1, 0, 0, 0, + 0, 1, 0, 0, + 0, 0, 1, Zoff, + 0, 0, 0, 1, + }, S = { + Dx(screen->r)/2, 0, 0, 0, + 0, Dy(screen->r)/2, 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1, + }; + u32int c; + int nvistri, i; + + vistris = nil; + nvistri = 0; + mulm(Yrot, Xrot); + mulm(Zrot, Yrot); + mulm(RT, Zrot); + lockdisplay(display); + draw(screen, screen->r, display->black, nil, ZP); + for(i = 0; i < model.ntri; i++){ + trans.p0 = mulvecm(model.tris[i].p0, RT); + trans.p1 = mulvecm(model.tris[i].p1, RT); + trans.p2 = mulvecm(model.tris[i].p2, RT); + n = normvec3(crossvec( + subvec3(trans.p1, trans.p0), + subvec3(trans.p2, trans.p0))); + if(dotvec3(n, subvec3(trans.p0, Vec3(0, 0, 0))) < 0){ + trans.p0 = mulvecm(trans.p0, proj); + trans.p1 = mulvecm(trans.p1, proj); + trans.p2 = mulvecm(trans.p2, proj); + trans.p0 = addvec3(trans.p0, Vec3(1, 1, 0)); + trans.p1 = addvec3(trans.p1, Vec3(1, 1, 0)); + trans.p2 = addvec3(trans.p2, Vec3(1, 1, 0)); + trans.p0 = mulvecm(trans.p0, S); + trans.p1 = mulvecm(trans.p1, S); + trans.p2 = mulvecm(trans.p2, S); + c = 0xff*fabs(dotvec3(n, light)); + trans.tx = eallocimage(display, Rect(0, 0, 1, 1), screen->chan, 1, c<<24|c<<16|c<<8|0xff); + vistris = erealloc(vistris, ++nvistri*sizeof(Triangle3)); + vistris[nvistri-1] = trans; + } + } + qsort(vistris, nvistri, sizeof(Triangle3), depthcmp); + for(i = 0; i < nvistri; i++){ + filltriangle(screen, Trianpt( + toscreen(Vec(vistris[i].p0.x, vistris[i].p0.y)), + toscreen(Vec(vistris[i].p1.x, vistris[i].p1.y)), + toscreen(Vec(vistris[i].p2.x, vistris[i].p2.y)) + ), vistris[i].tx, ZP); + if(dowireframe) + triangle(screen, Trianpt( + toscreen(Vec(vistris[i].p0.x, vistris[i].p0.y)), + toscreen(Vec(vistris[i].p1.x, vistris[i].p1.y)), + toscreen(Vec(vistris[i].p2.x, vistris[i].p2.y)) + ), 0, display->black, ZP); + freeimage(vistris[i].tx); + } + free(vistris); + flushimage(display, 1); + unlockdisplay(display); +} + +void +rmb(void) +{ + enum { + DOWIREFRM, + }; + static char *items[] = { + [DOWIREFRM] "toggle wireframe", + nil, + }; + static Menu menu = { .item = items }; + + switch(menuhit(3, mctl, &menu, nil)){ + case DOWIREFRM: + dowireframe ^= 1; + break; + } + t0 = nsec(); +} + +void +mouse(void) +{ + if(mctl->buttons & 4) + rmb(); +} + +void +key(Rune r) +{ + switch(r){ + case Kdel: + case 'q': + threadexitsall(nil); + case Kpgup: + Zoff += 0.2; + break; + case Kpgdown: + Zoff -= 0.2; + break; + } +} + +void +resized(void) +{ + lockdisplay(display); + if(getwindow(display, Refnone) < 0) + fprint(2, "can't reattach to window\n"); + unlockdisplay(display); + orig = Pt(screen->r.min.x, screen->r.max.y); + a = (double)Dy(screen->r)/Dx(screen->r); + proj[0][0] = a*(1/tan(FOV/2*DEG)); + redraw(); +} + +void +scrsynproc(void *) +{ + threadsetname("scrsynproc"); + for(;;){ + rlock(&worldlock); + redraw(); + runlock(&worldlock); + sleep(SEC/FPS); + } +} + +void +usage(void) +{ + fprint(2, "usage: %s\n", argv0); + threadexitsall("usage"); +} + +void +threadmain(int argc, char *argv[]) +{ + Rune r; + + fmtinstall('V', Vfmt); + fmtinstall('T', Tfmt); + ARGBEGIN{ + default: usage(); + }ARGEND; + + if(initdraw(nil, nil, "threedee") < 0) + sysfatal("initdraw: %r"); + if((mctl = initmouse(nil, screen)) == nil) + sysfatal("initmouse: %r"); + if((kctl = initkeyboard(nil)) == nil) + sysfatal("initkeyboard: %r"); + orig = Pt(screen->r.min.x, screen->r.max.y); + basis = Vec(1, -1); + Znear = 0.1; + Zfar = 1000; + Zoff = 2; + a = (double)Dy(screen->r)/Dx(screen->r); + proj[0][0] = a*(1/tan(FOV/2*DEG)); + proj[1][1] = 1/tan(FOV/2*DEG); + proj[2][2] = Zfar / (Zfar + Znear); + proj[2][3] = -Zfar * Znear / (Zfar + Znear); + proj[3][2] = 1; + light = Vec3(0, 0, -1); + if((model.ntri = objread("mdl/rocket.obj", &model.tris)) < 0) + sysfatal("objread: %r"); + display->locking = 1; + unlockdisplay(display); + proccreate(scrsynproc, nil, STACK); + ω = 1; + t0 = nsec(); + for(;;){ + enum {MOUSE, RESIZE, KBD}; + Alt a[] = { + {mctl->c, &mctl->Mouse, CHANRCV}, + {mctl->resizec, nil, CHANRCV}, + {kctl->c, &r, CHANRCV}, + {nil, nil, CHANNOBLK} + }; + wlock(&worldlock); + switch(alt(a)){ + case MOUSE: mouse(); break; + case RESIZE: resized(); break; + case KBD: key(r); break; + } + Δt = (nsec()-t0)/1e9; + θ += ω*Δt; + t0 += Δt*1e9; + wunlock(&worldlock); + sleep(SEC/FPS); + } +} diff --git a/matrix.c b/matrix.c new file mode 100644 index 0000000..e38722c --- /dev/null +++ b/matrix.c @@ -0,0 +1,82 @@ +#include <u.h> +#include <libc.h> +#include <draw.h> +#include "dat.h" + +void +addm(Matrix a, Matrix b) +{ + int i, j; + + for(i = 0; i < 4; i++) + for(j = 0; j < 4; j++) + a[i][j] += b[i][j]; +} + +void +subm(Matrix a, Matrix b) +{ + int i, j; + + for(i = 0; i < 4; i++) + for(j = 0; j < 4; j++) + a[i][j] -= b[i][j]; +} + +void +mulm(Matrix a, Matrix b) +{ + int i, j, k; + Matrix r; + + for(i = 0; i < 4; i++) + for(j = 0; j < 4; j++){ + r[i][j] = 0; + for(k = 0; k < 4; k++) + r[i][j] += a[i][k]*b[k][j]; + } + for(i = 0; i < 4; i++) + for(j = 0; j < 4; j++) + a[i][j] = r[i][j]; +} + +void +transm(Matrix m) +{ + int i, j; + double tmp; + + for(i = 0; i < 4; i++) + for(j = i; j < 4; j++){ + tmp = m[i][j]; + m[i][j] = m[j][i]; + m[j][i] = tmp; + } +} + +double +detm(Matrix m) +{ + return m[0][0]*(m[1][1]*m[2][2] - m[1][2]*m[2][1]) + + m[0][1]*(m[1][2]*m[2][0] - m[1][0]*m[2][2]) + + m[0][2]*(m[1][0]*m[2][1] - m[1][1]*m[2][0]); +} + +Vector3 +mulvecm(Vector3 v, Matrix m) +{ + Vector3 r; + double w; + + r.x = v.x * m[0][0] + v.y * m[0][1] + v.z * m[0][2] + m[0][3]; + r.y = v.x * m[1][0] + v.y * m[1][1] + v.z * m[1][2] + m[1][3]; + r.z = v.x * m[2][0] + v.y * m[2][1] + v.z * m[2][2] + m[2][3]; + w = v.x * m[3][0] + v.y * m[3][1] + v.z * m[3][2] + m[3][3]; + + if(w == 0) + return r; + r.x /= w; + r.y /= w; + r.z /= w; + return r; +} diff --git a/mdl/box.obj b/mdl/box.obj new file mode 100644 index 0000000..5653b60 --- /dev/null +++ b/mdl/box.obj @@ -0,0 +1,30 @@ +# Vertices: 8 +# Points: 0 +# Lines: 0 +# Faces: 6 +# Materials: 1 + +o 1 + +# Vertex list + +v -0.5 -0.5 0.5 +v -0.5 -0.5 -0.5 +v -0.5 0.5 -0.5 +v -0.5 0.5 0.5 +v 0.5 -0.5 0.5 +v 0.5 -0.5 -0.5 +v 0.5 0.5 -0.5 +v 0.5 0.5 0.5 + +# Point/Line/Face list + +usemtl Default +f 4 3 2 1 +f 2 6 5 1 +f 3 7 6 2 +f 8 7 3 4 +f 5 8 4 1 +f 6 7 8 5 + +# End of file diff --git a/mdl/rocket.obj b/mdl/rocket.obj new file mode 100644 index 0000000..834fdbc --- /dev/null +++ b/mdl/rocket.obj @@ -0,0 +1,143 @@ +# Blender v2.79 (sub 0) OBJ File: '' +# www.blender.org +v -0.334186 0.372621 -0.333268 +v -0.334186 0.370788 0.335102 +v 0.334186 0.370788 0.335102 +v 0.334186 0.372621 -0.333268 +v -0.334186 -0.295749 -0.335102 +v -0.334186 -0.297582 0.333269 +v 0.334186 -0.297582 0.333268 +v 0.334186 -0.295749 -0.335102 +v -0.334186 -0.695815 -0.336199 +v -0.334186 -0.697648 0.332171 +v 0.334186 -0.695815 -0.336199 +v 0.334186 -0.697648 0.332171 +v -0.120197 -0.754088 -0.122369 +v -0.120197 -0.754748 0.118024 +v 0.120197 -0.754088 -0.122369 +v 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2971 7764 +f 7761 7764 7765 +f 7762 7765 7766 +f 2971 2970 7767 +f 7764 7767 7768 +f 7765 7768 7769 +f 2970 97 791 +f 7767 791 790 +f 7768 790 789 +f 3164 7772 647 +f 7772 7775 646 +f 7775 7778 645 +f 488 3404 7770 +f 3162 7770 7771 +f 3163 7771 7772 +f 3404 3403 7773 +f 7770 7773 7774 +f 7771 7774 7775 +f 3403 3402 7776 +f 7773 7776 7777 +f 7774 7777 7778 +f 3402 40 498 +f 7776 498 499 +f 7777 499 500 @@ -0,0 +1,16 @@ +</$objtype/mkfile + +BIN=/$objtype/bin/ +TARG=threedee +OFILES=\ + main.$O\ + util.$O\ + matrix.$O\ + vector3.$O\ + vector.$O\ + triangle.$O\ + obj.$O + +HFILES=dat.h fns.h + +</sys/src/cmd/mkone @@ -0,0 +1,65 @@ +#include <u.h> +#include <libc.h> +#include <ctype.h> +#include <bio.h> +#include <draw.h> +#include "dat.h" +#include "fns.h" + +Vector3 *verts; +Triangle3 *tris; +int nvert, ntri; +int lineno; + +int +objread(char *f, Triangle3 **mesh) +{ + Biobuf *bin; + char *s; + int idx; + double *coord; + Vector3 *vert; + + bin = Bopen(f, OREAD); + if(bin == nil) + sysfatal("Bopen: %r"); + while((s = Brdline(bin, '\n')) != nil){ + lineno++; + if(*s == 'v'){ + verts = erealloc(verts, ++nvert*sizeof(Vector3)); + coord = (double *)(verts+nvert-1); + while(*s != '\n' && (Vector3 *)coord-verts < nvert){ + while(isspace(*++s)) + ; + *coord++ = strtod(s, &s); + } + if(coord-(double *)(verts+nvert-1) < 3){ + werrstr("%s:%d insufficient coordinates", f, lineno); + goto error; + } + } + if(*s == 'f'){ + tris = erealloc(tris, ++ntri*sizeof(Triangle3)); + vert = (Vector3 *)(tris+ntri-1); + while(*s != '\n' && (Triangle3 *)vert-tris < ntri){ + while(isspace(*++s)) + ; + idx = strtol(s, &s, 0); + if(idx > nvert){ + werrstr("%s:%d insufficient vertices", f, lineno); + goto error; + } + *vert++ = verts[idx-1]; + } + } + } + *mesh = tris; + free(verts); + Bterm(bin); + return ntri; +error: + free(verts); + free(tris); + Bterm(bin); + return -1; +} diff --git a/readme.md b/readme.md new file mode 100644 index 0000000..48e1785 --- /dev/null +++ b/readme.md @@ -0,0 +1,4 @@ +# Threedee + +Threedee is a 3D graphics demo I developed back in 2019. It is the +precursor to the 3dee project and its libraries. diff --git a/triangle.c b/triangle.c new file mode 100644 index 0000000..5301956 --- /dev/null +++ b/triangle.c @@ -0,0 +1,58 @@ +#include <u.h> +#include <libc.h> +#include <draw.h> +#include "dat.h" +#include "fns.h" + +Triangle +Trian(int x0, int y0, int x1, int y1, int x2, int y2) +{ + return (Triangle){Pt(x0, y0), Pt(x1, y1), Pt(x2, y2)}; +} + +Triangle +Trianpt(Point p0, Point p1, Point p2) +{ + return (Triangle){p0, p1, p2}; +}; + +Point +centroid(Triangle t) +{ + return divpt(addpt(t.p0, addpt(t.p1, t.p2)), 3); +} + +void +triangle(Image *dst, Triangle t, int thick, Image *src, Point sp) +{ + Point pl[4]; + + pl[0] = t.p0; + pl[1] = t.p1; + pl[2] = t.p2; + pl[3] = pl[0]; + + poly(dst, pl, nelem(pl), 0, 0, thick, src, sp); +} + +void +filltriangle(Image *dst, Triangle t, Image *src, Point sp) +{ + Point pl[4]; + + pl[0] = t.p0; + pl[1] = t.p1; + pl[2] = t.p2; + pl[3] = pl[0]; + + fillpoly(dst, pl, nelem(pl), 0, src, sp); +} + +Triangle +rotatriangle(Triangle t, double θ, Point c) +{ + t.p0 = rotatept(t.p0, θ, c); + t.p1 = rotatept(t.p1, θ, c); + t.p2 = rotatept(t.p2, θ, c); + return t; +} @@ -0,0 +1,29 @@ +#include <u.h> +#include <libc.h> +#include <draw.h> +#include "dat.h" +#include "fns.h" + +double +round(double n) +{ + return floor(n + 0.5); +} + +Point +rotatept(Point p, double θ, Point c) +{ + Point r; + + p = subpt(p, c); + r.x = round(p.x*cos(θ) - p.y*sin(θ)); + r.y = round(p.x*sin(θ) + p.y*cos(θ)); + r = addpt(r, c); + return r; +} + +double +hypot3(double x, double y, double z) +{ + return hypot(x, hypot(y, z)); +} diff --git a/vector.c b/vector.c new file mode 100644 index 0000000..3595c1f --- /dev/null +++ b/vector.c @@ -0,0 +1,60 @@ +#include <u.h> +#include <libc.h> +#include <draw.h> +#include "dat.h" +#include "fns.h" + +Vector +Vec(double x, double y) +{ + return (Vector){x, y}; +} + +Vector +addvec(Vector v, Vector u) +{ + return (Vector){v.x+u.x, v.y+u.y}; +} + +Vector +subvec(Vector v, Vector u) +{ + return (Vector){v.x-u.x, v.y-u.y}; +} + +Vector +mulvec(Vector v, double s) +{ + return (Vector){v.x*s, v.y*s}; +} + +double +dotvec(Vector v, Vector u) +{ + return v.x*u.x + v.y*u.y; +} + +Vector +normvec(Vector v) +{ + double len; + + len = hypot(v.x, v.y); + if(len == 0) + return (Vector){0, 0}; + v.x /= len; + v.y /= len; + return v; +} + +Vector +rotatevec(Vector p, double θ, Vector c) +{ + Vector r; + + p = subvec(p, c); + r.x = p.x*cos(θ) - p.y*sin(θ); + r.y = p.x*sin(θ) + p.y*cos(θ); + r = addvec(r, c); + return r; +} diff --git a/vector3.c b/vector3.c new file mode 100644 index 0000000..933716e --- /dev/null +++ b/vector3.c @@ -0,0 +1,59 @@ +#include <u.h> +#include <libc.h> +#include <draw.h> +#include "dat.h" +#include "fns.h" + +Vector3 +Vec3(double x, double y, double z) +{ + return (Vector3){x, y, z}; +} + +Vector3 +addvec3(Vector3 v, Vector3 u) +{ + return (Vector3){v.x+u.x, v.y+u.y, v.z+u.z}; +} + +Vector3 +subvec3(Vector3 v, Vector3 u) +{ + return (Vector3){v.x-u.x, v.y-u.y, v.z-u.z}; +} + +Vector3 +mulvec3(Vector3 v, double s) +{ + return (Vector3){v.x*s, v.y*s, v.z*s}; +} + +double +dotvec3(Vector3 v, Vector3 u) +{ + return v.x*u.x + v.y*u.y + v.z*u.z; +} + +Vector3 +crossvec(Vector3 v, Vector3 u) +{ + return (Vector3){ + v.y*u.z - v.z*u.y, + v.z*u.x - v.x*u.z, + v.x*u.y - v.y*u.x + }; +} + +Vector3 +normvec3(Vector3 v) +{ + double len; + + len = hypot3(v.x, v.y, v.z); + if(len == 0) + return (Vector3){0, 0, 0}; + v.x /= len; + v.y /= len; + v.z /= len; + return v; +} |