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];

	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\" stroke-width=\"0.1px\"/>\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,
	int at_head
)
{
	if (at_head)
	{
		new_g->work_next = g->work_next;
		g->work_next = new_g;
		return;
	}

	// go to the end of the line
	while (g->work_next)
		g = g->work_next;
	g->work_next = new_g;
}


static poly_t * poly_root;
static float poly_min[2], poly_max[2];

static inline int
v2_eq(
	const float p0[],
	const float p1[]
)
{
	const float dx = p0[0] - p1[0];
	const float dy = p0[1] - p1[1];

	// are the points within epsilon of each other?
	if (-EPS < dx && dx < EPS
	&&  -EPS < dy && dy < EPS)
		return 1;

	// nope, not equal
	return 0;
}



// Returns 1 if the lines intersect, otherwise 0. In addition, if the lines 
// intersect the intersection point may be stored in the floats i_x and i_y.
int
get_line_intersection(
	float p0_x,
	float p0_y,
	float p1_x,
	float p1_y, 
	float p2_x,
	float p2_y,
	float p3_x,
	float p3_y,
	float *i_x,
	float *i_y
)
{
	float s1_x = p1_x - p0_x;
	float s1_y = p1_y - p0_y;
	float s2_x = p3_x - p2_x;
	float s2_y = p3_y - p2_y;

	float s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y))
		/ (-s2_x * s1_y + s1_x * s2_y);

	float t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x))
		/ (-s2_x * s1_y + s1_x * s2_y);

	if (s > EPS && s < 1-EPS && t > EPS && t < 1-EPS)
	{
		fprintf(stderr, "collision: %f,%f->%f,%f %f,%f->%f,%f == %f,%f\n",
			p0_x, p0_y,
			p1_x, p1_y,
			p2_x, p2_y,
			p3_x, p3_y,
			s,
			t
		);

		// Collision detected
		if (i_x != NULL)
			*i_x = p0_x + (t * s1_x);
		if (i_y != NULL)
			*i_y = p0_y + (t * s1_y);
		return 1;
	}

	return 0; // No collision
}


int
intersect(
	const float p00[],
	const float p01[],
	const float p10[],
	const float p11[]
)
{
	// special case; if this is the same line, it does not intersect
	if (v2_eq(p00, p10) && v2_eq(p01, p11))
		return 0;
	if (v2_eq(p01, p10) && v2_eq(p00, p11))
		return 0;

	return get_line_intersection(
		p00[0],
		p00[1],
		p01[0],
		p01[1],
		p10[0],
		p10[1],
		p11[0],
		p11[1],
		NULL,
		NULL
	);
}


/** Check to see if two triangles overlap */
int
overlap_poly(
	const poly_t * const g1,
	const poly_t * const g2
)
{
	if (intersect(g1->p[0], g1->p[1], g2->p[0], g2->p[1]))
		return 1;
	if (intersect(g1->p[0], g1->p[1], g2->p[1], g2->p[2]))
		return 1;
	if (intersect(g1->p[0], g1->p[1], g2->p[2], g2->p[0]))
		return 1;

	if (intersect(g1->p[1], g1->p[2], g2->p[0], g2->p[1]))
		return 1;
	if (intersect(g1->p[1], g1->p[2], g2->p[1], g2->p[2]))
		return 1;
	if (intersect(g1->p[1], g1->p[2], g2->p[2], g2->p[0]))
		return 1;

	if (intersect(g1->p[2], g1->p[0], g2->p[0], g2->p[1]))
		return 1;
	if (intersect(g1->p[2], g1->p[0], g2->p[1], g2->p[2]))
		return 1;
	if (intersect(g1->p[2], g1->p[0], g2->p[2], g2->p[0]))
		return 1;

	return 0;
}


/** Check to see if any triangles overlap */
int
overlap_check(
	const poly_t * g,
	const poly_t * const new_g
)
{
	// special case -- if the root is the same as the one that we
	// are checking, then it does not overlap
	if (g == new_g)
		return 0;

	while (g)
	{
		if (overlap_poly(g, new_g))
			return 1;
		g = g->work_next;
	}

	return 0;
}


/** 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;

	// update the group's bounding box
	for (int i = 0 ; i < 3 ; i++)
	{
		const float px = g->p[i][0];
		const float py = g->p[i][1];

		if (px < poly_min[0]) poly_min[0] = px;
		if (px > poly_max[0]) poly_max[0] = px;

		if (py < poly_min[1]) poly_min[1] = py;
		if (py > poly_max[1]) poly_max[1] = py;
	}
		

	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] == 0)
			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
		);

		if (overlap_check(poly_root, g2))
		{
			free(g2);
			continue;
		}

		// no overlap, add it to the current group
		g->next[i] = g2;
		g2->next[0] = g;
		f2->used = 1;

		// if g2 is a coplanar triangle, process it now rather than
		// defering the work.
		if (f->coplanar[edge] == 0)
			enqueue(g, g2, 1);
		else
			enqueue(g, g2, 0);
	}
    }

	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] < 0)
		{
			// draw a mountain score line since they are not coplanar
			svg_line("#00FF00", g->p[i], g->p[(i+1) % 3]);
		} else
		if (f->coplanar[edge] > 0)
		{
			// draw a mountain score line since they are not coplanar
			svg_line("#0000FF", g->p[i], g->p[(i+1) % 3]);
		} else {
			// draw a shadow line since they are coplanar
			//svg_line("#F0F0F0", 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);
	}
}


/* Returns the 0 for coplanar, negative for mountain, positive for valley.
 * (approximates the angle between two triangles that share one edge).
 */
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: %f\n", f1, f2, check ? "yes" : "no", dot);
	return (int) dot;
}


/** 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 = { };

	float last_x = 0;
	float last_y = 0;

	srand48(getpid());

	const int offset = lrand48();
	for (int i = 0 ; i < num_triangles ; i++)
	{
		face_t * const f = &faces[(i+offset) % num_triangles];
		if (f->used)
			continue;
		poly_t g = {
			.face	= f,
			.start_edge	= 0,
		};
		poly_position(&g, &origin, 0, 0, 0);

		// set the root of the new group
		poly_root = &g;
		poly_min[0] = poly_min[1] = 0;
		poly_max[0] = poly_max[1] = 0;

		fprintf(stderr, "\n\n\n****** New group %p\n", poly_root);

		poly_t * iter = &g;
		while (iter)
		{
			poly_build(iter);
			iter = iter->work_next;
		}

		// offset the poly so that it doesn't overlap the ones
		// we've already generated. only shift in Y.
		float off_x = last_x - poly_min[0];
		float off_y = last_y - poly_min[1];
		last_y = off_y + poly_max[1];

		printf("<g transform=\"translate(%f %f)\">\n", off_x, off_y);
		poly_print(&g);
		printf("</g>\n");
	}

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

	return 0;
}