papercraft/unfold.c

/** \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];
};


/* 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,
	float a,
	float x,
	float y
)
{
	p[0] = cos(a) * x - sin(a) * y;
	p[1] = sin(a) * x + cos(a) * y;
}


/* Rotate and translate a triangle */
void
poly_position(
	poly_t * const g,
	float trans_x,
	float trans_y,
	float rot
)
{
	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);

	g->rot = rot;
	g->a = a;
	g->x2 = x2;
	g->y2 = y2;

	rotate(g->p[0], rot, trans_x +  0, trans_y +  0);
	rotate(g->p[1], rot, trans_x +  a, trans_y +  0);
	rotate(g->p[2], rot, trans_x + x2, trans_y + y2);
}


/** 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 = 180;
		} 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];
		g->next[edge] = g2;
		g2->next[g2->start_edge] = g;

		poly_position(
			g2,
			g->rot + rotate, 
			g->p[0][0] + trans_x,
			g->p[0][1] + trans_y
		);

		// \todo: CHECK FOR OVERLAP!

		poly_build(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>\n");
	for (int i = 0 ; i < 3 ; i++)
	{
		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[(0+start_edge) % 3])
		{
			// draw a score line since they are not coplanar
			svg_line("#00FF00", 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]);
	}

	// 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");
	for (int i = 0 ; i < num_triangles ; i++)
	{
		face_t * const f = &faces[i];
		if (f->used)
			continue;
		poly_t g;
		g.face = f;
		poly_position(&g, 0, 0, 0);

		poly_build(&g);

		printf("<g>\n");
		poly_print(&g);
		printf("</g>\n");
	}

	printf("</svg>\n");

	return 0;
}