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seamoptimizer.h
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seamoptimizer.h
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/***********************************************************
* A single header file lightmap seam optimization library *
* https://github.com/ands/seamoptimizer *
* no warranty implied | use at your own risk *
* author: Andreas Mantler (ands) | last change: 05.03.2017 *
* *
* License: *
* This software is in the public domain. *
* Where that dedication is not recognized, *
* you are granted a perpetual, irrevocable license to copy *
* and modify this file however you want. *
***********************************************************/
#ifndef SEAMOPTIMIZER_H
#define SEAMOPTIMIZER_H
#ifndef SO_CALLOC
#include <malloc.h> // calloc, free, alloca
#define SO_CALLOC(count, size) calloc(count, size)
#define SO_FREE(ptr) free(ptr)
#endif
typedef int so_bool;
#define SO_FALSE 0
#define SO_TRUE 1
typedef struct so_seam_t so_seam_t;
// API
// so_seams_find:
// Find all seams according to the specified triangulated geometry and its texture coordinates.
// This searches for edges that are shared by triangles, but are disjoint in UV space.
// positions: triangle array 3d positions ((x0, y0, z0), (x1, y1, z1), (x2, y2, z2)), ((x0, y0, z0), (x1, y1, z1), (x2, y2, z2)), ...
// texcoords: triangle array 2d uv coords ( (u0, v0), (u1, v1), (u2, v2)), ( (u0, v0), (u1, v1), (u2, v2)), ...
// vertices: total number of vertices ( = triangles * 3)
// cosNormalThreshold controls at which angles between neighbour triangles a seam should be considered.
// if dot(triangle A normal, triangle B normal) > cosNormalThreshold then the seam is included into the returned set.
// data, w, h, c specifies the lightmap data (data should be a w * h * c array of floats).
// w = lightmap width, h = lightmap height, c = number of lightmap channels (1..4).
// returns a linked list of the found seams.
// Warning: The data may be modified to fill empty (zeroed) edge texels with one of their closest neighbours if they are empty!
so_seam_t *so_seams_find(
float *positions, float *texcoords, int vertices,
float cosNormalThreshold,
float *data, int w, int h, int c);
// so_seam_optimize:
// Optimize a single seam. Seams can be optimized in parallel on different threads.
// lambda: Weight that controls the deviation from the original color values (must be > 0).
// Higher values => Less deviation from the original edge colors => more obvious seams.
// Too low values => Optimizer may just choose black as the perfect color for all seam pixels.
// returns whether the optimization was successful.
so_bool so_seam_optimize(
so_seam_t *seam,
float *data, int w, int h, int c,
float lambda);
// so_seam_next: Retrieves the next seam in the linked list.
so_seam_t *so_seam_next(
so_seam_t *seam);
// so_seams_free: Free the resources for all seams in the list.
void so_seams_free(
so_seam_t *seams);
#endif
////////////////////// END OF HEADER //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#ifdef SEAMOPTIMIZER_IMPLEMENTATION
#undef SEAMOPTIMIZER_IMPLEMENTATION
#include <stdlib.h> // qsort
#include <stdio.h> // printf (TODO)
#include <string.h> // memcpy
#include <stdint.h>
#include <math.h>
#include <float.h>
#include <assert.h>
#define SO_EPSILON 0.00001f
#ifdef _DEBUG
#define SO_NOT_ZERO(v) (v > SO_EPSILON || v < -SO_EPSILON) // a lot faster in debug
#else
#define SO_NOT_ZERO(v) (fabsf(v) > SO_EPSILON) // faster in release
#endif
#ifdef SO_APPROX_RSQRT
#include "xmmintrin.h"
static inline float so_rsqrtf(float v)
{
return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(v)));
}
#else
static inline float so_rsqrtf(float v)
{
return 1.0f / sqrtf(v);
}
#endif
static inline int16_t so_min16i (int16_t a, int16_t b) { return a < b ? a : b; }
static inline int16_t so_max16i (int16_t a, int16_t b) { return a > b ? a : b; }
static inline float so_minf (float a, float b) { return a < b ? a : b; }
static inline float so_maxf (float a, float b) { return a > b ? a : b; }
static inline float so_absf (float a ) { return a < 0.0f ? -a : a; }
typedef struct so_vec2 { float x, y; } so_vec2;
static inline so_vec2 so_v2i (int x, int y) { so_vec2 v = { (float)x, (float)y }; return v; }
static inline so_vec2 so_v2 (float x, float y) { so_vec2 v = { x, y }; return v; }
static inline so_vec2 so_add2 (so_vec2 a, so_vec2 b) { return so_v2(a.x + b.x, a.y + b.y); }
static inline so_vec2 so_sub2 (so_vec2 a, so_vec2 b) { return so_v2(a.x - b.x, a.y - b.y); }
static inline so_vec2 so_mul2 (so_vec2 a, so_vec2 b) { return so_v2(a.x * b.x, a.y * b.y); }
static inline so_vec2 so_scale2 (so_vec2 a, float b) { return so_v2(a.x * b, a.y * b); }
static inline float so_length2sq (so_vec2 a ) { return a.x * a.x + a.y * a.y; }
static inline float so_length2 (so_vec2 a ) { return sqrtf(so_length2sq(a)); }
typedef struct so_vec3 { float x, y, z; } so_vec3;
static inline so_vec3 so_v3 (float x, float y, float z) { so_vec3 v = { x, y, z }; return v; }
static inline so_vec3 so_sub3 (so_vec3 a, so_vec3 b) { return so_v3(a.x - b.x, a.y - b.y, a.z - b.z); }
static inline so_vec3 so_mul3 (so_vec3 a, so_vec3 b) { return so_v3(a.x * b.x, a.y * b.y, a.z * b.z); }
static inline so_vec3 so_scale3 (so_vec3 a, float b) { return so_v3(a.x * b, a.y * b, a.z * b); }
static inline so_vec3 so_div3 (so_vec3 a, float b) { return so_scale3(a, 1.0f / b); }
static inline so_vec3 so_min3 (so_vec3 a, so_vec3 b) { return so_v3(so_minf(a.x, b.x), so_minf(a.y, b.y), so_minf(a.z, b.z)); }
static inline so_vec3 so_max3 (so_vec3 a, so_vec3 b) { return so_v3(so_maxf(a.x, b.x), so_maxf(a.y, b.y), so_maxf(a.z, b.z)); }
static inline float so_dot3 (so_vec3 a, so_vec3 b) { return a.x * b.x + a.y * b.y + a.z * b.z; }
static inline so_vec3 so_cross3 (so_vec3 a, so_vec3 b) { return so_v3(a.y * b.z - b.y * a.z, a.z * b.x - b.z * a.x, a.x * b.y - b.x * a.y); }
static inline float so_length3sq (so_vec3 a ) { return a.x * a.x + a.y * a.y + a.z * a.z; }
static inline float so_length3 (so_vec3 a ) { return sqrtf(so_length3sq(a)); }
static inline so_vec3 so_normalize3(so_vec3 a ) { return so_div3(a, so_length3(a)); }
//#define SO_CHECK_FOR_MEMORY_LEAKS // check for memory leaks. don't use this in multithreaded code!
#ifdef SO_CHECK_FOR_MEMORY_LEAKS
static uint64_t so_allocated = 0;
static uint64_t so_allocated_max = 0;
static void *so_alloc_void(size_t size)
{
void *memory = SO_CALLOC(1, size + sizeof(size_t));
(*(size_t*)memory) = size;
so_allocated += size;
if (so_allocated > so_allocated_max)
so_allocated_max = so_allocated;
return (size_t*)memory + 1;
}
static void so_free(void *memory)
{
size_t size = ((size_t*)memory)[-1];
so_allocated -= size;
SO_FREE(((size_t*)memory) - 1);
}
#else
static void *so_alloc_void(size_t size)
{
return SO_CALLOC(1, size);
}
static void so_free(void *memory)
{
SO_FREE(memory);
}
#endif
#define so_alloc(type, count) ((type*)so_alloc_void(sizeof(type) * (count)))
static inline so_bool so_accumulate_texel(float *sums, int x, int y, float *data, int w, int h, int c)
{
so_bool exists = SO_FALSE;
for (int i = 0; i < c; i++)
{
float v = data[(y * w + x) * c + i];
sums[i] += v;
exists |= v > 0.0f;
}
return exists;
}
static void so_fill_with_closest(int x, int y, float *data, int w, int h, int c, int depth = 2)
{
assert(c <= 4);
for (int i = 0; i < c; i++)
if (data[(y * w + x) * c + i] > 0.0f)
return;
float sums[4] = {};
int n = 0;
if (x > 0 && so_accumulate_texel(sums, x - 1, y, data, w, h, c)) n++;
if (x + 1 < w && so_accumulate_texel(sums, x + 1, y, data, w, h, c)) n++;
if (y > 0 && so_accumulate_texel(sums, x, y - 1, data, w, h, c)) n++;
if (y + 1 < h && so_accumulate_texel(sums, x, y + 1, data, w, h, c)) n++;
if (!n && depth)
{
--depth;
if (x > 0)
{
so_fill_with_closest(x - 1, y, data, w, h, c, depth);
if (so_accumulate_texel(sums, x - 1, y, data, w, h, c)) n++;
}
if (x + 1 < w)
{
so_fill_with_closest(x + 1, y, data, w, h, c, depth);
if (so_accumulate_texel(sums, x + 1, y, data, w, h, c)) n++;
}
if (y > 0)
{
so_fill_with_closest(x, y - 1, data, w, h, c, depth);
if (so_accumulate_texel(sums, x, y - 1, data, w, h, c)) n++;
}
if (y + 1 < h)
{
so_fill_with_closest(x, y + 1, data, w, h, c, depth);
if (so_accumulate_texel(sums, x, y + 1, data, w, h, c)) n++;
}
}
if (n)
{
float ni = 1.0f / (float)n;
for (int i = 0; i < c; i++)
data[(y * w + x) * c + i] = sums[i] * ni;
}
}
typedef struct
{
int16_t x, y;
} so_texel_t;
static inline int so_texel_cmp(const void *l, const void *r)
{
const so_texel_t *lt = (const so_texel_t*)l;
const so_texel_t *rt = (const so_texel_t*)r;
if (lt->y < rt->y) return -1;
if (lt->y > rt->y) return 1;
if (lt->x < rt->x) return -1;
if (lt->x > rt->x) return 1;
return 0;
}
typedef struct
{
so_texel_t texels[4];
float weights[4];
} so_bilinear_sample_t;
typedef struct
{
so_bilinear_sample_t sides[2];
} so_stitching_point_t;
typedef struct
{
so_texel_t *texels;
uint32_t count;
uint32_t capacity;
} so_texel_set_t;
static inline uint32_t so_texel_hash(so_texel_t texel, uint32_t capacity)
{
return (texel.y * 104173 + texel.x * 86813) % capacity;
}
static void so_texel_set_add(so_texel_set_t *set, so_texel_t *texels, int entries, int arrayLength = 0)
{
if (set->count + entries > set->capacity * 3 / 4) // leave some free space to avoid having many collisions
{
int newCapacity = set->capacity > 64 ? set->capacity * 2 : 64;
while (set->count + entries > newCapacity * 3 / 4)
newCapacity *= 2;
so_texel_t *newTexels = so_alloc(so_texel_t, newCapacity);
for (int i = 0; i < newCapacity; i++)
newTexels[i].x = -1;
if (set->texels)
{
for (int i = 0; i < set->capacity; i++) // rehash all old texels
{
if (set->texels[i].x != -1)
{
uint32_t hash = so_texel_hash(set->texels[i], newCapacity);
while (newTexels[hash].x != -1) // collisions
hash = (hash + 1) % newCapacity;
newTexels[hash] = set->texels[i];
}
}
so_free(set->texels);
}
set->texels = newTexels;
set->capacity = newCapacity;
}
if (arrayLength == 0)
arrayLength = entries;
for (int i = 0; i < arrayLength; i++)
{
if (texels[i].x != -1)
{
uint32_t hash = so_texel_hash(texels[i], set->capacity);
while (set->texels[hash].x != -1) // collisions
{
if (set->texels[hash].x == texels[i].x && set->texels[hash].y == texels[i].y)
break; // texel is already in the set
hash = (hash + 1) % set->capacity;
}
if (set->texels[hash].x == -1)
{
set->texels[hash] = texels[i];
set->count++;
}
}
}
}
static so_bool so_texel_set_contains(so_texel_set_t *set, so_texel_t texel)
{
uint32_t hash = so_texel_hash(texel, set->capacity);
while (set->texels[hash].x != -1) // entries with same hash
{
if (set->texels[hash].x == texel.x && set->texels[hash].y == texel.y)
return SO_TRUE; // texel is already in the set
hash = (hash + 1) % set->capacity;
}
return SO_FALSE;
}
static void so_texel_set_free(so_texel_set_t *set)
{
so_free(set->texels);
*set = {0};
}
typedef struct
{
so_stitching_point_t *points;
uint32_t count;
uint32_t capacity;
} so_stitching_points_t;
static void so_stitching_points_alloc(so_stitching_points_t *points, uint32_t n)
{
points->points = so_alloc(so_stitching_point_t, n);
points->capacity = n;
points->count = 0;
}
static void so_stitching_points_free(so_stitching_points_t *points)
{
so_free(points->points);
*points = {0};
}
static void so_stitching_points_add(so_stitching_points_t *points, so_stitching_point_t *point)
{
assert(points->count < points->capacity);
points->points[points->count++] = *point;
}
static void so_stitching_points_append(so_stitching_points_t *points, so_stitching_points_t *other)
{
so_stitching_point_t *newPoints = so_alloc(so_stitching_point_t, points->capacity + other->capacity);
memcpy(newPoints, points->points, sizeof(so_stitching_point_t) * points->count);
memcpy(newPoints + points->count, other->points, sizeof(so_stitching_point_t) * other->count);
so_free(points->points);
points->points = newPoints;
points->capacity = points->capacity + other->capacity;
points->count = points->count + other->count;
}
struct so_seam_t
{
int16_t x_min, y_min, x_max, y_max;
so_texel_set_t texels;
so_stitching_points_t stitchingPoints;
so_seam_t *next;
};
so_seam_t *so_seam_next(so_seam_t *seam)
{
return seam->next;
}
static void so_seam_alloc(so_seam_t *seam, uint32_t stitchingPointCount)
{
so_stitching_points_alloc(&seam->stitchingPoints, stitchingPointCount);
}
static void so_seam_free(so_seam_t *seam)
{
so_texel_set_free(&seam->texels);
so_stitching_points_free(&seam->stitchingPoints);
}
static void so_seam_add(so_seam_t *seam, so_stitching_point_t *point)
{
for (int side = 0; side < 2; side++)
{
for (int texel = 0; texel < 4; texel++)
{
so_texel_t t = point->sides[side].texels[texel];
seam->x_min = t.x < seam->x_min ? t.x : seam->x_min;
seam->y_min = t.y < seam->y_min ? t.y : seam->y_min;
seam->x_max = t.x > seam->x_max ? t.x : seam->x_max;
seam->y_max = t.y > seam->y_max ? t.y : seam->y_max;
}
so_texel_set_add(&seam->texels, point->sides[side].texels, 4);
}
so_stitching_points_add(&seam->stitchingPoints, point);
}
static so_bool so_seams_intersect(so_seam_t *a, so_seam_t *b)
{
// compare bounding boxes first
if (a->x_min > b->x_max || b->x_min >= a->x_max ||
a->y_min > b->y_max || b->y_min >= a->y_max)
return SO_FALSE;
// bounds intersect -> check each individual texel for intersection
if (a->texels.capacity > b->texels.capacity) // swap so that we always loop over the smaller set
{
so_seam_t *tmp = a;
a = b;
b = tmp;
}
for (int i = 0; i < a->texels.capacity; i++)
if (a->texels.texels[i].x != -1)
if (so_texel_set_contains(&b->texels, a->texels.texels[i]))
return SO_TRUE;
return SO_FALSE;
}
static void so_seams_in_place_merge(so_seam_t *dst, so_seam_t *src)
{
// expand bounding box
dst->x_min = src->x_min < dst->x_min ? src->x_min : dst->x_min;
dst->y_min = src->y_min < dst->y_min ? src->y_min : dst->y_min;
dst->x_max = src->x_max > dst->x_max ? src->x_max : dst->x_max;
dst->y_max = src->y_max > dst->y_max ? src->y_max : dst->y_max;
// insert src elements
so_texel_set_add(&dst->texels, src->texels.texels, src->texels.count, src->texels.capacity);
so_stitching_points_append(&dst->stitchingPoints, &src->stitchingPoints);
}
static void so_seams_add_seam(so_seam_t **seams, so_vec2 a0, so_vec2 a1, so_vec2 b0, so_vec2 b1, float *data, int w, int h, int c)
{
so_vec2 s = so_v2i(w, h);
a0 = so_mul2(a0, s);
a1 = so_mul2(a1, s);
b0 = so_mul2(b0, s);
b1 = so_mul2(b1, s);
so_vec2 ad = so_sub2(a1, a0);
so_vec2 bd = so_sub2(b1, b0);
float l = so_length2(ad);
int iterations = (int)(l * 5.0f); // TODO: is this the best value?
float step = 1.0f / iterations;
so_seam_t currentSeam = {0};
currentSeam.x_min = w; currentSeam.y_min = h;
currentSeam.x_max = 0; currentSeam.y_max = 0;
so_seam_alloc(¤tSeam, iterations + 1);
for (int i = 0; i <= iterations; i++)
{
float t = i * step;
so_vec2 a = so_add2(a0, so_scale2(ad, t));
so_vec2 b = so_add2(b0, so_scale2(bd, t));
int16_t ax = (int16_t)roundf(a.x), ay = (int16_t)roundf(a.y);
int16_t bx = (int16_t)roundf(b.x), by = (int16_t)roundf(b.y);
float au = a.x - ax, av = a.y - ay, nau = 1.0f - au, nav = 1.0f - av;
float bu = b.x - bx, bv = b.y - by, nbu = 1.0f - bu, nbv = 1.0f - bv;
so_texel_t ta0 = { ax , ay };
so_texel_t ta1 = { so_min16i(ax + 1, w - 1), ay };
so_texel_t ta2 = { ax , so_min16i(ay + 1, h - 1) };
so_texel_t ta3 = { so_min16i(ax + 1, w - 1), so_min16i(ay + 1, h - 1) };
so_texel_t tb0 = { bx , by };
so_texel_t tb1 = { so_min16i(bx + 1, w - 1), by };
so_texel_t tb2 = { bx , so_min16i(by + 1, h - 1) };
so_texel_t tb3 = { so_min16i(bx + 1, w - 1), so_min16i(by + 1, h - 1) };
so_fill_with_closest(ta0.x, ta0.y, data, w, h, c);
so_fill_with_closest(ta1.x, ta1.y, data, w, h, c);
so_fill_with_closest(ta2.x, ta2.y, data, w, h, c);
so_fill_with_closest(ta3.x, ta3.y, data, w, h, c);
so_fill_with_closest(tb0.x, tb0.y, data, w, h, c);
so_fill_with_closest(tb1.x, tb1.y, data, w, h, c);
so_fill_with_closest(tb2.x, tb2.y, data, w, h, c);
so_fill_with_closest(tb3.x, tb3.y, data, w, h, c);
so_stitching_point_t sp;
sp.sides[0].texels[0] = ta0;
sp.sides[0].texels[1] = ta1;
sp.sides[0].texels[2] = ta2;
sp.sides[0].texels[3] = ta3;
sp.sides[0].weights[0] = nau * nav;
sp.sides[0].weights[1] = au * nav;
sp.sides[0].weights[2] = nau * av;
sp.sides[0].weights[3] = au * av;
sp.sides[1].texels[0] = tb0;
sp.sides[1].texels[1] = tb1;
sp.sides[1].texels[2] = tb2;
sp.sides[1].texels[3] = tb3;
sp.sides[1].weights[0] = nbu * nbv;
sp.sides[1].weights[1] = bu * nbv;
sp.sides[1].weights[2] = nbu * bv;
sp.sides[1].weights[3] = bu * bv;
so_seam_add(¤tSeam, &sp);
}
so_seam_t *dstSeam = 0;
for (so_seam_t **seam = seams; *seam; seam = &(*seam)->next)
{
retry:
if (so_seams_intersect(¤tSeam, *seam))
{
if (!dstSeam) // found a seam that the edge is connected to -> add current edge to that seam
{
so_seams_in_place_merge(*seam, ¤tSeam);
dstSeam = *seam;
}
else // found another seam that the edge is connected to -> merge those seams
{
so_seams_in_place_merge(dstSeam, *seam);
// remove current seam from seams
so_seam_t *toDelete = *seam;
*seam = (*seam)->next;
so_seam_free(toDelete);
so_free(toDelete);
if (*seam)
goto retry; // don't move to next since we already did that by deleting the current seam
else
break;
}
}
}
if (!dstSeam) // did not find a seam that the edge is connected to -> make a new one
{
currentSeam.next = *seams;
*seams = so_alloc(so_seam_t, 1);
**seams = currentSeam;
}
else
so_seam_free(¤tSeam);
}
void so_seams_free(so_seam_t *seams)
{
so_seam_t *seam = seams;
while (seam)
{
so_seam_t *next = seam->next;
so_seam_free(seam);
so_free(seam);
seam = next;
}
#ifdef SO_CHECK_FOR_MEMORY_LEAKS
assert(so_allocated == 0);
printf("Allocated max %d MB. Not freed: %d bytes.\n", so_allocated_max / (1024 * 1024), so_allocated);
printf("These results are only correct if the lib was used single-threaded.\n");
so_allocated_max = 0;
#endif
}
static int so_should_optimize(so_vec3 *tria, so_vec3 *trib, float cosThreshold)
{
so_vec3 n0 = so_normalize3(so_cross3(so_sub3(tria[1], tria[0]), so_sub3(tria[2], tria[0])));
so_vec3 n1 = so_normalize3(so_cross3(so_sub3(trib[1], trib[0]), so_sub3(trib[2], trib[0])));
return so_absf(so_dot3(n0, n1)) > cosThreshold;
}
so_seam_t *so_seams_find(float *positions, float *texcoords, int vertices, float cosNormalThreshold, float *data, int w, int h, int c)
{
so_vec3 *pos = (so_vec3*)positions;
so_vec2 *uv = (so_vec2*)texcoords;
so_vec3 bbmin = so_v3(FLT_MAX, FLT_MAX, FLT_MAX);
so_vec3 bbmax = so_v3(-FLT_MAX, -FLT_MAX, -FLT_MAX);
int *hashmap = so_alloc(int, vertices * 2);
for (int i = 0; i < vertices; i++)
{
bbmin = so_min3(bbmin, pos[i]);
bbmax = so_max3(bbmax, pos[i]);
hashmap[i * 2 + 0] = -1;
hashmap[i * 2 + 1] = -1;
}
so_vec3 bbscale = so_v3(15.9f / bbmax.x, 15.9f / bbmax.y, 15.9f / bbmax.z);
so_seam_t *seams = 0;
for (int i0 = 0; i0 < vertices; i0++)
{
int tri = i0 - (i0 % 3);
int i1 = tri + ((i0 + 1) % 3);
int i2 = tri + ((i0 + 2) % 3);
so_vec3 p = so_mul3(so_sub3(pos[i0], bbmin), bbscale);
int hash = (281 * (int)p.x + 569 * (int)p.y + 1447 * (int)p.z) % (vertices * 2);
while (hashmap[hash] >= 0)
{
int oi0 = hashmap[hash];
#define SO_EQUAL(a, b) so_length3sq(so_sub3(pos[a], pos[b])) < 0.0000001f
if (SO_EQUAL(oi0, i0))
{
int otri = oi0 - (oi0 % 3);
int oi1 = otri + ((oi0 + 1) % 3);
int oi2 = otri + ((oi0 + 2) % 3);
if (SO_EQUAL(oi1, i1) && so_should_optimize(pos + tri, pos + otri, cosNormalThreshold))
so_seams_add_seam(&seams, uv[i0], uv[i1], uv[oi0], uv[oi1], data, w, h, c);
//else if (SO_EQUAL(oi1, i2) && so_should_optimize(pos + tri, pos + otri, cosNormalThreshold)) // this will already be detected by the other side of the seam!
// so_seams_add_seam(&seams, uv[i0], uv[i2], uv[oi0], uv[oi1], data, w, h, c);
else if (SO_EQUAL(oi2, i1) && so_should_optimize(pos + tri, pos + otri, cosNormalThreshold))
so_seams_add_seam(&seams, uv[i0], uv[i1], uv[oi0], uv[oi2], data, w, h, c);
//break;
}
if (++hash == vertices * 2)
hash = 0;
}
hashmap[hash] = i0;
}
so_free(hashmap);
return seams;
}
static int so_texel_binary_search(so_texel_t *texels, int n, so_texel_t toFind)
{
int n_half = n / 2;
so_texel_t *center = texels + n_half;
if (toFind.y == center->y && toFind.x == center->x)
return n_half;
if (n <= 1)
return -1;
if (toFind.y < center->y || (toFind.y == center->y && toFind.x < center->x))
return so_texel_binary_search(texels, n_half, toFind);
else
{
int result = so_texel_binary_search(center + 1, n - n_half - 1, toFind);
return result == -1 ? -1 : n_half + 1 + result;
}
}
typedef struct
{
int index;
float value;
} so_sparse_entry_t;
static int so_sparse_entry_cmp(const void *a, const void *b)
{
so_sparse_entry_t *ae = (so_sparse_entry_t*)a;
so_sparse_entry_t *be = (so_sparse_entry_t*)b;
return ae->index - be->index;
}
typedef struct
{
so_sparse_entry_t *entries;
int count;
int capacity;
} so_sparse_entries_t;
static void so_sparse_matrix_alloc(so_sparse_entries_t *matrix, int capacity)
{
matrix->entries = so_alloc(so_sparse_entry_t, capacity);
matrix->capacity = capacity;
matrix->count = 0;
}
static void so_sparse_matrix_free(so_sparse_entries_t *matrix)
{
so_free(matrix->entries);
*matrix = { 0 };
}
static void so_sparse_matrix_add(so_sparse_entries_t *matrix, int index, float value)
{
if (matrix->count == matrix->capacity)
{
int newCapacity = matrix->capacity * 2;
if (newCapacity < 64)
newCapacity = 64;
so_sparse_entry_t *newEntries = so_alloc(so_sparse_entry_t, newCapacity);
for (int i = 0; i < matrix->count; i++)
newEntries[i] = matrix->entries[i];
so_free(matrix->entries);
matrix->entries = newEntries;
matrix->capacity = newCapacity;
}
int entryIndex = matrix->count++;
matrix->entries[entryIndex].index = index;
matrix->entries[entryIndex].value = value;
}
static void so_sparse_matrix_add(so_sparse_entries_t *matrix, so_sparse_entry_t *entry)
{
so_sparse_matrix_add(matrix, entry->index, entry->value);
}
static void so_sparse_matrix_sort(so_sparse_entries_t *matrix)
{
qsort(matrix->entries, matrix->count, sizeof(so_sparse_entry_t), so_sparse_entry_cmp);
}
static so_bool so_sparse_matrix_advance_to_index(so_sparse_entries_t *matrix, int *position, int index, float *outValue)
{
int localPosition = *position;
while (localPosition < matrix->count && matrix->entries[localPosition].index < index)
++localPosition;
*position = localPosition;
if (localPosition < matrix->count && matrix->entries[localPosition].index == index)
{
*outValue = matrix->entries[localPosition].value;
return SO_TRUE;
}
return SO_FALSE;
}
static inline uint32_t so_sparse_entry_hash(int entryIndex, uint32_t capacity)
{
return (entryIndex * 104173) % capacity;
}
static void so_sparse_entry_set_alloc(so_sparse_entries_t *set, int capacity)
{
set->entries = so_alloc(so_sparse_entry_t, capacity);
for (int i = 0; i < capacity; i++)
set->entries[i].index = -1;
set->capacity = capacity;
set->count = 0;
}
static so_sparse_entry_t *so_sparse_entry_set_get_or_add(so_sparse_entries_t *set, int index)
{
if (set->count + 1 > set->capacity * 3 / 4) // leave some free space to avoid having many collisions
{
int newCapacity = set->capacity >= 64 ? set->capacity * 2 : 64;
so_sparse_entry_t *newEntries = so_alloc(so_sparse_entry_t, newCapacity);
for (int i = 0; i < newCapacity; i++)
newEntries[i].index = -1;
for (int i = 0; i < set->capacity; i++) // rehash all old entries
{
if (set->entries[i].index != -1)
{
uint32_t hash = so_sparse_entry_hash(set->entries[i].index, newCapacity);
while (newEntries[hash].index != -1) // collisions
hash = (hash + 1) % newCapacity;
newEntries[hash] = set->entries[i];
}
}
so_free(set->entries);
set->entries = newEntries;
set->capacity = newCapacity;
}
uint32_t hash = so_sparse_entry_hash(index, set->capacity);
while (set->entries[hash].index != -1) // collisions
{
if (set->entries[hash].index == index)
return &set->entries[hash]; // entry is already in the set
hash = (hash + 1) % set->capacity;
}
if (set->entries[hash].index == -1) // make new entry
{
set->entries[hash].index = index;
set->entries[hash].value = 0.0f;
set->count++;
return &set->entries[hash];
}
return 0; // shouldn't happen
}
static so_sparse_entries_t so_matrix_At_times_A(const float *A, const int *sparseIndices, int maxRowIndices, int m, int n)
{
so_sparse_entries_t AtA;
so_sparse_entry_set_alloc(&AtA, (n / 16) * (n / 16));
// compute lower left triangle only since the result is symmetric
for (int k = 0; k < m; k++)
{
const float *srcPtr = A + k * maxRowIndices;
const int *indexPtr = sparseIndices + k * maxRowIndices;
for (int i = 0; i < maxRowIndices; i++)
{
int index_i = indexPtr[i];
if (index_i < 0) break;
float v = srcPtr[i];
//float *dstPtr = AtA + index_i * n;
for (int j = 0; j < maxRowIndices; j++)
{
int index_j = indexPtr[j];
if (index_j < 0) break;
//dstPtr[index_j] += v * srcPtr[j];
int index = index_i * n + index_j;
so_sparse_entry_t *entry = so_sparse_entry_set_get_or_add(&AtA, index);
entry->value += v * srcPtr[j];
}
}
}
// compaction step (make a compact array from the scattered hash set values)
for (int i = 0, j = 0; i < AtA.capacity; i++)
if (AtA.entries[i].index != -1)
AtA.entries[j++] = AtA.entries[i];
// sort by index -> this is a sparse matrix now
so_sparse_matrix_sort(&AtA);
return AtA;
}
static void so_matrix_At_times_b(const float *A, int m, int n, const float *b, float *Atb, const int *sparseIndices, int maxRowIndices)
{
memset(Atb, 0, sizeof(float) * n);
for (int j = 0; j < m; j++)
{
const int *rowIndices = sparseIndices + j * maxRowIndices;
for (int i = 0; i < maxRowIndices; i++)
{
int index = rowIndices[i];
if (index < 0) break;
Atb[index] += A[j * maxRowIndices + i] * b[j];
}
}
}
static so_sparse_entries_t so_matrix_cholesky_prepare(so_sparse_entries_t *AtA, int n)
{
// dense
//for (int i = 0; i < n; i++)
//{
// float *a = L + i * n;
// for (int j = 0; j <= i; j++)
// {
// float *b = L + j * n;
// float sum = A[i * n + j];// + (i == j ? 0.0001 : 0.0); // some regularization
// for (int k = 0; k < j; k++)
// sum -= a[k] * b[k];
// if (i > j)
// a[j] = sum / b[j];
// else // i == j
// {
// if (sum <= 0.0)
// return SO_FALSE;
// a[i] = sqrtf(sum);
// }
// }
//}
// sparse
int *indices_i;
float *row_i;
float *invDiag;
if (n > 4096)
{
indices_i = so_alloc(int, n);
row_i = so_alloc(float, n);
invDiag = so_alloc(float, n);
}
else
{
indices_i = (int*)alloca(sizeof(int) * n);
row_i = (float*)alloca(sizeof(float) * n);
invDiag = (float*)alloca(sizeof(float) * n);
}
so_sparse_entries_t L;
so_sparse_matrix_alloc(&L, (n / 16) * (n / 16));
int AtAindex = 0;
for (int i = 0; i < n; i++)
{
int index_i_count = 0;
int row_j_index = 0;
for (int j = 0; j <= i; j++)
{
//float sum = A[i * n + j]; // + (i == j ? 0.0001 : 0.0); // regularization
int index = i * n + j;
float sum = 0.0f;
so_sparse_matrix_advance_to_index(AtA, &AtAindex, index, &sum);
for (int k = 0; k < index_i_count; k++)
{
int index_i = indices_i[k];
float Lvalue;
if (so_sparse_matrix_advance_to_index(&L, &row_j_index, j * n + index_i, &Lvalue))
sum -= row_i[index_i] * Lvalue;
}
if (i == j)
{
if (sum <= 0.0f)
{
so_sparse_matrix_free(&L);
return L;
}
invDiag[i] = so_rsqrtf(sum);
}
if (SO_NOT_ZERO(sum))
{
row_i[j] = sum * invDiag[j];
indices_i[index_i_count++] = j;
so_sparse_matrix_add(&L, index, row_i[j]);
}
else
row_i[j] = 0.0f;
}
}
if (n > 4096)
{
so_free(indices_i);
so_free(row_i);
so_free(invDiag);
}
return L;
}
static void so_matrix_cholesky_solve(so_sparse_entries_t *Lrows, so_sparse_entries_t *Lcols, float *x, const float *b, int n)
{
float *y = (float*)alloca(sizeof(float) * n);
// L * y = b
int Lindex = 0;
for (int i = 0; i < n; i++)
{
float sum = b[i];
while (Lindex < Lrows->count && Lrows->entries[Lindex].index < i * (n + 1))
{
sum -= Lrows->entries[Lindex].value * y[Lrows->entries[Lindex].index - i * n];
++Lindex;
}
assert(Lrows->entries[Lindex].index == i * (n + 1));
y[i] = sum / Lrows->entries[Lindex].value;
++Lindex;
}
// L' * x = y
Lindex = Lcols->count - 1;
for (int i = n - 1; i >= 0; i--)
{
float sum = y[i];
while (Lindex >= 0 && Lcols->entries[Lindex].index > i * (n + 1))
{
sum -= Lcols->entries[Lindex].value * x[Lcols->entries[Lindex].index - i * n];
--Lindex;
}
assert(Lcols->entries[Lindex].index == i * (n + 1));
x[i] = sum / Lcols->entries[Lindex].value;
--Lindex;
}
}
so_bool so_seam_optimize(so_seam_t *seam, float *data, int w, int h, int c, float lambda)
{
so_texel_set_t *texels = &seam->texels;
so_stitching_points_t *stitchingPoints = &seam->stitchingPoints;
size_t m = stitchingPoints->count;
size_t n = texels->count;
void *memoryBlock = so_alloc_void(
sizeof(so_texel_t) * n +
sizeof(float) * (m + n) * 8 +
sizeof(int) * (m + n) * 8 +
sizeof(float) * (m + n) +
sizeof(float) * n +
sizeof(float) * n);