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papercraft/unfold.c

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/** \file
* Unfold an STL file into a set of laser-cutable polygons.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <unistd.h>
#include <math.h>
#include <err.h>
#include <assert.h>
#include "v3.h"
#ifndef M_PI
#define M_PI 3.1415926535897932384
#endif
typedef struct
{
char header[80];
uint32_t num_triangles;
} __attribute__((__packed__))
stl_header_t;
typedef struct
{
v3_t normal;
v3_t p[3];
uint16_t attr;
} __attribute__((__packed__))
stl_face_t;
typedef struct face face_t;
typedef struct poly poly_t;
struct face
{
float sides[3];
face_t * next[3];
int next_edge[3];
int coplanar[3];
int used;
};
// once this triangle has been used, it will be placed
// in a polygon group and fixed in a position relative to that group
struct poly
{
int start_edge;
int printed;
// local coordinates of the triangle vertices
float a;
float x2;
float y2;
float rot;
// absolute coordintes of the triangle vertices
float p[3][2];
face_t * face;
poly_t * next[3];
poly_t * work_next;
};
/* Compare two edges in two triangles.
*
* note that if the windings are all the same, the edges will
* compare in the opposite order (for example, the edge from 0 to 1
* compares to the edge from 2 to 1 in the other triangle).
*/
static int
edge_eq2(
const stl_face_t * const t0,
const stl_face_t * const t1,
int e0,
int e1
)
{
const v3_t * const v00 = &t0->p[e0];
const v3_t * const v01 = &t0->p[(e0+1) % 3];
const v3_t * const v10 = &t1->p[e1];
const v3_t * const v11 = &t1->p[(e1+1) % 3];
if (v3_eq(v00, v11) && v3_eq(v01, v10))
return 1;
return 0;
}
void
svg_line(
const char * color,
float * p1,
float * p2
)
{
printf("<line x1=\"%f\" y1=\"%f\" x2=\"%f\" y2=\"%f\" stroke=\"%s\"/>\n",
p1[0],
p1[1],
p2[0],
p2[1],
color
);
}
void
rotate(
float * p,
const float * origin,
float a,
float x,
float y
)
{
p[0] = cos(a) * x - sin(a) * y + origin[0];
p[1] = sin(a) * x + cos(a) * y + origin[1];
}
/* Rotate and translate a triangle */
void
poly_position(
poly_t * const g,
const poly_t * const g_src,
float rot,
float trans_x,
float trans_y
)
{
face_t * const f = g->face;
const int start_edge = g->start_edge;
float a = f->sides[(start_edge + 0) % 3];
float c = f->sides[(start_edge + 1) % 3];
float b = f->sides[(start_edge + 2) % 3];
float x2 = (a*a + b*b - c*c) / (2*a);
float y2 = sqrt(b*b - x2*x2);
// translate by trans_x/trans_y in the original ref frame
// to get the origin point
float origin[2];
rotate(origin, g_src->p[0], g_src->rot, trans_x, trans_y);
g->rot = g_src->rot + rot;
g->a = a;
g->x2 = x2;
g->y2 = y2;
fprintf(stderr, "%p %d %f %f %f %f => %f %f %f\n", f, start_edge, g->rot*180/M_PI, a, b, c, x2, y2, rot);
rotate(g->p[0], origin, g->rot, 0, 0);
rotate(g->p[1], origin, g->rot, a, 0);
rotate(g->p[2], origin, g->rot, x2, y2);
}
static void
enqueue(
poly_t * g,
poly_t * const new_g
)
{
while (g->work_next)
g = g->work_next;
g->work_next = new_g;
}
/** recursively try to fix up the triangles.
*
* returns the maximum number of triangles added
*/
int
poly_build(
poly_t * const g
)
{
face_t * const f = g->face;
const int start_edge = g->start_edge;
f->used = 1;
fprintf(stderr, "%p: adding to poly\n", f);
for(int pass = 0 ; pass < 2 ; pass++)
{
// for each edge, find the triangle that matches
for (int i = 0 ; i < 3 ; i++)
{
const int edge = (i + start_edge) % 3;
face_t * const f2 = f->next[edge];
assert(f2 != NULL);
if (f2->used)
continue;
if (pass == 0 && !f->coplanar[edge])
continue;
// create a group that translates and rotates
// such that it lines up with this edge
float trans_x, trans_y, rotate;
if (i == 0)
{
trans_x = g->a;
trans_y = 0;
rotate = M_PI;
} else
if (i == 1)
{
trans_x = g->x2;
trans_y = g->y2;
rotate = -atan2(g->y2, g->a - g->x2);
} else
if (i == 2)
{
trans_x = 0;
trans_y = 0;
rotate = atan2(g->y2, g->x2);
} else {
errx(EXIT_FAILURE, "edge %d invalid?\n", i);
}
// position this one translated and rotated
poly_t * const g2 = calloc(1, sizeof(*g2));
g2->face = f2;
g2->start_edge = f->next_edge[edge];
poly_position(
g2,
g,
rotate,
trans_x,
trans_y
);
// \todo: CHECK FOR OVERLAP!
g->next[i] = g2;
g2->next[0] = g;
f2->used = 1;
enqueue(g, g2);
}
}
return 0;
}
void
poly_print(
poly_t * const g
)
{
face_t * const f = g->face;
const int start_edge = g->start_edge;
g->printed = 1;
// draw this triangle;
// if the edge is an outside, which means that the group
// has no next element, draw a cut line. If there is an
// adjacent neighbor and it is not coplanar, draw a score line
printf("<g><!-- %p %d %f %f->%p %f->%p %f->%p -->\n",
f,
g->start_edge, g->rot * 180/M_PI,
f->sides[0],
f->next[0],
f->sides[1],
f->next[1],
f->sides[2],
f->next[2]
);
for (int i = 0 ; i < 3 ; i++)
{
const int edge = (start_edge + i) % 3;
poly_t * const next = g->next[i];
if (!next)
{
// draw a cut line
svg_line("#FF0000", g->p[i], g->p[(i+1) % 3]);
continue;
}
if (next->printed)
continue;
if (f->coplanar[edge])
{
// draw a shadow line since they are coplanar
svg_line("#F0F0F0", g->p[i], g->p[(i+1) % 3]);
} else {
// draw a score line since they are not coplanar
svg_line("#0000FF", g->p[i], g->p[(i+1) % 3]);
}
}
printf("</g>\n");
for (int i = 0 ; i < 3 ; i++)
{
poly_t * const next = g->next[i];
if (!next || next->printed)
continue;
poly_print(next);
}
}
int
coplanar_check(
const stl_face_t * const f1,
const stl_face_t * const f2
)
{
// find the four distinct points
v3_t x1 = f1->p[0];
v3_t x2 = f1->p[1];
v3_t x3 = f1->p[2];
v3_t x4;
for (int i = 0 ; i < 3 ; i++)
{
x4 = f2->p[i];
if (v3_eq(&x1, &x4))
continue;
if (v3_eq(&x2, &x4))
continue;
if (v3_eq(&x3, &x4))
continue;
break;
}
// (x3-x1) . ((x2-x1) X (x4-x3)) == 0
v3_t dx31 = v3_sub(x3, x1);
v3_t dx21 = v3_sub(x2, x1);
v3_t dx43 = v3_sub(x4, x3);
v3_t cross = v3_cross(dx21, dx43);
float dot = v3_dot(dx31, cross);
int check = -EPS < dot && dot < +EPS;
//fprintf( stderr, "%p %p %s\n", f1, f2, check ? "yes" : "no");
return check;
}
/** Translate a list of STL triangles into a connected graph of faces.
*
* If there are any triangles that do not have three connected edges,
* the first error will be reported and NULL will be returned.
*/
face_t *
stl2faces(
const stl_face_t * const stl_faces,
const int num_triangles
)
{
face_t * const faces = calloc(num_triangles, sizeof(*faces));
// convert the stl triangles into faces
for (int i = 0 ; i < num_triangles ; i++)
{
const stl_face_t * const stl = &stl_faces[i];
face_t * const f = &faces[i];
f->sides[0] = v3_len(&stl->p[0], &stl->p[1]);
f->sides[1] = v3_len(&stl->p[1], &stl->p[2]);
f->sides[2] = v3_len(&stl->p[2], &stl->p[0]);
fprintf(stderr, "%p %f %f %f\n", f, f->sides[0], f->sides[1], f->sides[2]);
}
// look to see if there is a matching point
// in the faces that we've already built
for (int i = 0 ; i < num_triangles ; i++)
{
const stl_face_t * const stl = &stl_faces[i];
face_t * const f = &faces[i];
for (int j = 0 ; j < num_triangles ; j++)
{
if (i == j)
continue;
const stl_face_t * const stl2 = &stl_faces[j];
face_t * const f2 = &faces[j];
for (int edge = 0 ; edge < 3 ; edge++)
{
if (f->next[edge])
continue;
for (int edge2 = 0 ; edge2 < 3 ; edge2++)
{
if (f2->next[edge2])
continue;
if (!edge_eq2(stl, stl2, edge, edge2))
continue;
f->next[edge] = f2;
f->next_edge[edge] = edge2;
f2->next[edge2] = f;
f2->next_edge[edge2] = edge;
f->coplanar[edge] =
f2->coplanar[edge2] = coplanar_check(stl, stl2);
}
}
}
// all three edges should be matched
if (f->next[0] && f->next[1] && f->next[2])
continue;
fprintf(stderr, "%d missing edges?\n", i);
free(faces);
return NULL;
}
return faces;
}
int main(void)
{
const size_t max_len = 1 << 20;
uint8_t * const buf = calloc(max_len, 1);
ssize_t rc = read(0, buf, max_len);
if (rc == -1)
return EXIT_FAILURE;
const stl_header_t * const hdr = (const void*) buf;
const stl_face_t * const stl_faces = (const void*)(hdr+1);
const int num_triangles = hdr->num_triangles;
fprintf(stderr, "header: '%s'\n", hdr->header);
fprintf(stderr, "num: %d\n", num_triangles);
face_t * const faces = stl2faces(stl_faces, num_triangles);
// we now have a graph that shows the connection between
// all of the faces and their sizes. start trying to build
// non-overlapping groups of them
printf("<svg xmlns=\"http://www.w3.org/2000/svg\">\n");
poly_t origin = { };
for (int i = 0 ; i < num_triangles ; i++)
{
face_t * const f = &faces[i];
if (f->used)
continue;
poly_t g = {
.face = f,
.start_edge = 0,
};
poly_position(&g, &origin, 0, 0, 0);
poly_t * iter = &g;
while (iter)
{
poly_build(iter);
iter = iter->work_next;
}
printf("<g>\n");
poly_print(&g);
printf("</g>\n");
}
printf("</svg>\n");
return 0;
}
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