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Simplify.h
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Simplify.h
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/////////////////////////////////////////////
//
// Mesh Simplification Tutorial
//
// (C) by Sven Forstmann in 2014
//
// License : MIT
// http://opensource.org/licenses/MIT
//
// https://github.com/sp4cerat/Fast-Quadric-Mesh-Simplification
//
// 5/2016: Chris Rorden created minimal version for OSX/Linux/Windows compile
//#include <iostream>
//#include <stddef.h>
//#include <functional>
//#include <sys/stat.h>
//#include <stdbool.h>
#include <string.h>
//#include <ctype.h>
//#include <float.h>
#include <stdio.h>
#include <stdlib.h>
#include <map>
#include <vector>
#include <string>
#include <math.h>
#include <float.h> //FLT_EPSILON, DBL_EPSILON
#include <unordered_map>
#define loopi(start_l, end_l) for (int i = start_l; i < end_l; ++i)
#define loopi(start_l, end_l) for (int i = start_l; i < end_l; ++i)
#define loopj(start_l, end_l) for (int j = start_l; j < end_l; ++j)
#define loopk(start_l, end_l) for (int k = start_l; k < end_l; ++k)
struct vector3
{
double x, y, z;
};
struct vec3f
{
double x, y, z;
inline vec3f(void) {}
// inline vec3f operator =( vector3 a )
// { vec3f b ; b.x = a.x; b.y = a.y; b.z = a.z; return b;}
inline vec3f(vector3 a)
{
x = a.x;
y = a.y;
z = a.z;
}
inline vec3f(const double X, const double Y, const double Z)
{
x = X;
y = Y;
z = Z;
}
inline vec3f operator+(const vec3f &a) const
{
return vec3f(x + a.x, y + a.y, z + a.z);
}
inline vec3f operator+=(const vec3f &a) const
{
return vec3f(x + a.x, y + a.y, z + a.z);
}
inline vec3f operator*(const double a) const
{
return vec3f(x * a, y * a, z * a);
}
inline vec3f operator*(const vec3f a) const
{
return vec3f(x * a.x, y * a.y, z * a.z);
}
inline vec3f v3() const
{
return vec3f(x, y, z);
}
inline vec3f operator=(const vector3 a)
{
x = a.x;
y = a.y;
z = a.z;
return *this;
}
inline vec3f operator=(const vec3f a)
{
x = a.x;
y = a.y;
z = a.z;
return *this;
}
inline vec3f operator/(const vec3f a) const
{
return vec3f(x / a.x, y / a.y, z / a.z);
}
inline vec3f operator-(const vec3f &a) const
{
return vec3f(x - a.x, y - a.y, z - a.z);
}
inline vec3f operator/(const double a) const
{
return vec3f(x / a, y / a, z / a);
}
inline double dot(const vec3f &a) const
{
return a.x * x + a.y * y + a.z * z;
}
inline vec3f cross(const vec3f &a, const vec3f &b)
{
x = a.y * b.z - a.z * b.y;
y = a.z * b.x - a.x * b.z;
z = a.x * b.y - a.y * b.x;
return *this;
}
inline double angle(const vec3f &v)
{
vec3f a = v, b = *this;
double dot = v.x * x + v.y * y + v.z * z;
double len = a.length() * b.length();
if (len == 0)
len = 0.00001f;
double input = dot / len;
if (input < -1)
input = -1;
if (input > 1)
input = 1;
return (double)acos(input);
}
inline double angle2(const vec3f &v, const vec3f &w)
{
vec3f a = v, b = *this;
double dot = a.x * b.x + a.y * b.y + a.z * b.z;
double len = a.length() * b.length();
if (len == 0)
len = 1;
vec3f plane;
plane.cross(b, w);
if (plane.x * a.x + plane.y * a.y + plane.z * a.z > 0)
return (double)-acos(dot / len);
return (double)acos(dot / len);
}
inline vec3f rot_x(double a)
{
double yy = cos(a) * y + sin(a) * z;
double zz = cos(a) * z - sin(a) * y;
y = yy;
z = zz;
return *this;
}
inline vec3f rot_y(double a)
{
double xx = cos(-a) * x + sin(-a) * z;
double zz = cos(-a) * z - sin(-a) * x;
x = xx;
z = zz;
return *this;
}
inline void clamp(double min, double max)
{
if (x < min)
x = min;
if (y < min)
y = min;
if (z < min)
z = min;
if (x > max)
x = max;
if (y > max)
y = max;
if (z > max)
z = max;
}
inline vec3f rot_z(double a)
{
double yy = cos(a) * y + sin(a) * x;
double xx = cos(a) * x - sin(a) * y;
y = yy;
x = xx;
return *this;
}
inline vec3f invert()
{
x = -x;
y = -y;
z = -z;
return *this;
}
inline vec3f frac()
{
return vec3f(
x - double(int(x)),
y - double(int(y)),
z - double(int(z)));
}
inline vec3f integer()
{
return vec3f(
double(int(x)),
double(int(y)),
double(int(z)));
}
inline double length() const
{
return (double)sqrt(x * x + y * y + z * z);
}
inline vec3f normalize(double desired_length = 1)
{
double square = sqrt(x * x + y * y + z * z);
/*
if (square <= 0.00001f )
{
x=1;y=0;z=0;
return *this;
}*/
// double len = desired_length / square;
x /= square;
y /= square;
z /= square;
return *this;
}
static vec3f normalize(vec3f a);
static void random_init();
static double random_double();
static vec3f random();
static int random_number;
double random_double_01(double a)
{
double rnf = a * 14.434252 + a * 364.2343 + a * 4213.45352 + a * 2341.43255 + a * 254341.43535 + a * 223454341.3523534245 + 23453.423412;
int rni = ((int)rnf) % 100000;
return double(rni) / (100000.0f - 1.0f);
}
vec3f random01_fxyz()
{
x = (double)random_double_01(x);
y = (double)random_double_01(y);
z = (double)random_double_01(z);
return *this;
}
};
vec3f barycentric(const vec3f &p, const vec3f &a, const vec3f &b, const vec3f &c)
{
vec3f v0 = b - a;
vec3f v1 = c - a;
vec3f v2 = p - a;
double d00 = v0.dot(v0);
double d01 = v0.dot(v1);
double d11 = v1.dot(v1);
double d20 = v2.dot(v0);
double d21 = v2.dot(v1);
double denom = d00 * d11 - d01 * d01;
double v = (d11 * d20 - d01 * d21) / denom;
double w = (d00 * d21 - d01 * d20) / denom;
double u = 1.0 - v - w;
return vec3f(u, v, w);
}
vec3f interpolate(const vec3f &p, const vec3f &a, const vec3f &b, const vec3f &c, const vec3f attrs[3])
{
vec3f bary = barycentric(p, a, b, c);
vec3f out = vec3f(0, 0, 0);
out = out + attrs[0] * bary.x;
out = out + attrs[1] * bary.y;
out = out + attrs[2] * bary.z;
return out;
}
double min(double v1, double v2)
{
return fmin(v1, v2);
}
class SymetricMatrix
{
public:
// Constructor
SymetricMatrix(double c = 0) { loopi(0, 10) m[i] = c; }
SymetricMatrix(double m11, double m12, double m13, double m14,
double m22, double m23, double m24,
double m33, double m34,
double m44)
{
m[0] = m11;
m[1] = m12;
m[2] = m13;
m[3] = m14;
m[4] = m22;
m[5] = m23;
m[6] = m24;
m[7] = m33;
m[8] = m34;
m[9] = m44;
}
// Make plane
SymetricMatrix(double a, double b, double c, double d)
{
m[0] = a * a;
m[1] = a * b;
m[2] = a * c;
m[3] = a * d;
m[4] = b * b;
m[5] = b * c;
m[6] = b * d;
m[7] = c * c;
m[8] = c * d;
m[9] = d * d;
}
double operator[](int c) const { return m[c]; }
// Determinant
double det(int a11, int a12, int a13,
int a21, int a22, int a23,
int a31, int a32, int a33)
{
double det = m[a11] * m[a22] * m[a33] + m[a13] * m[a21] * m[a32] + m[a12] * m[a23] * m[a31] - m[a13] * m[a22] * m[a31] - m[a11] * m[a23] * m[a32] - m[a12] * m[a21] * m[a33];
return det;
}
const SymetricMatrix operator+(const SymetricMatrix &n) const
{
return SymetricMatrix(m[0] + n[0], m[1] + n[1], m[2] + n[2], m[3] + n[3],
m[4] + n[4], m[5] + n[5], m[6] + n[6],
m[7] + n[7], m[8] + n[8],
m[9] + n[9]);
}
SymetricMatrix &operator+=(const SymetricMatrix &n)
{
m[0] += n[0];
m[1] += n[1];
m[2] += n[2];
m[3] += n[3];
m[4] += n[4];
m[5] += n[5];
m[6] += n[6];
m[7] += n[7];
m[8] += n[8];
m[9] += n[9];
return *this;
}
double m[10];
};
///////////////////////////////////////////
namespace Simplify
{
// Global Variables & Strctures
enum Attributes
{
NONE,
NORMAL = 2,
TEXCOORD = 4,
COLOR = 8
};
struct Triangle
{
int v[3];
double err[4];
int deleted, dirty, attr;
vec3f n;
vec3f uvs[3];
int material;
};
struct Vertex
{
vec3f p;
int tstart, tcount;
SymetricMatrix q;
int border;
};
struct Ref
{
int tid, tvertex;
};
std::vector<Triangle> triangles;
std::vector<Vertex> vertices;
std::vector<Ref> refs;
std::string mtllib;
std::vector<std::string> materials;
// Helper functions
double vertex_error(SymetricMatrix q, double x, double y, double z);
double calculate_error(int id_v1, int id_v2, vec3f &p_result);
bool flipped(vec3f p, int i0, int i1, Vertex &v0, Vertex &v1, std::vector<int> &deleted);
void update_uvs(int i0, const Vertex &v, const vec3f &p, std::vector<int> &deleted);
void update_triangles(int i0, Vertex &v, std::vector<int> &deleted, int &deleted_triangles);
void update_mesh(int iteration);
void compact_mesh();
//
// Main simplification function
//
// target_count : target nr. of triangles
// agressiveness : sharpness to increase the threshold.
// 5..8 are good numbers
// more iterations yield higher quality
//
void simplify_mesh(int target_count, double agressiveness = 7, bool verbose = false)
{
// init
loopi(0, triangles.size())
{
triangles[i].deleted = 0;
}
// main iteration loop
int deleted_triangles = 0;
std::vector<int> deleted0, deleted1;
int triangle_count = triangles.size();
// int iteration = 0;
// loop(iteration,0,100)
for (int iteration = 0; iteration < 100; iteration++)
{
if (triangle_count - deleted_triangles <= target_count)
break;
// update mesh once in a while
if (iteration % 5 == 0)
{
update_mesh(iteration);
}
// clear dirty flag
loopi(0, triangles.size()) triangles[i].dirty = 0;
//
// All triangles with edges below the threshold will be removed
//
// The following numbers works well for most models.
// If it does not, try to adjust the 3 parameters
//
double threshold = 0.000000001 * pow(double(iteration + 3), agressiveness);
// target number of triangles reached ? Then break
if ((verbose) && (iteration % 5 == 0))
{
printf("iteration %d - triangles %d threshold %g\n", iteration, triangle_count - deleted_triangles, threshold);
}
// remove vertices & mark deleted triangles
loopi(0, triangles.size())
{
Triangle &t = triangles[i];
if (t.err[3] > threshold)
continue;
if (t.deleted)
continue;
if (t.dirty)
continue;
loopj(0, 3) if (t.err[j] < threshold)
{
int i0 = t.v[j];
Vertex &v0 = vertices[i0];
int i1 = t.v[(j + 1) % 3];
Vertex &v1 = vertices[i1];
// Border check
if (v0.border != v1.border)
continue;
// Compute vertex to collapse to
vec3f p;
calculate_error(i0, i1, p);
deleted0.resize(v0.tcount); // normals temporarily
deleted1.resize(v1.tcount); // normals temporarily
// don't remove if flipped
if (flipped(p, i0, i1, v0, v1, deleted0))
continue;
if (flipped(p, i1, i0, v1, v0, deleted1))
continue;
if ((t.attr & TEXCOORD) == TEXCOORD)
{
update_uvs(i0, v0, p, deleted0);
update_uvs(i0, v1, p, deleted1);
}
// not flipped, so remove edge
v0.p = p;
v0.q = v1.q + v0.q;
int tstart = refs.size();
update_triangles(i0, v0, deleted0, deleted_triangles);
update_triangles(i0, v1, deleted1, deleted_triangles);
int tcount = refs.size() - tstart;
if (tcount <= v0.tcount)
{
// save ram
if (tcount)
memcpy(&refs[v0.tstart], &refs[tstart], tcount * sizeof(Ref));
}
else
// append
v0.tstart = tstart;
v0.tcount = tcount;
break;
}
// done?
if (triangle_count - deleted_triangles <= target_count)
break;
}
}
// clean up mesh
compact_mesh();
} // simplify_mesh()
void simplify_mesh_lossless(bool verbose = false)
{
// init
loopi(0, triangles.size()) triangles[i].deleted = 0;
// main iteration loop
int deleted_triangles = 0;
std::vector<int> deleted0, deleted1;
int triangle_count = triangles.size();
// int iteration = 0;
// loop(iteration,0,100)
for (int iteration = 0; iteration < 9999; iteration++)
{
// update mesh constantly
update_mesh(iteration);
// clear dirty flag
loopi(0, triangles.size()) triangles[i].dirty = 0;
//
// All triangles with edges below the threshold will be removed
//
// The following numbers works well for most models.
// If it does not, try to adjust the 3 parameters
//
double threshold = DBL_EPSILON; // 1.0E-3 EPS;
if (verbose)
{
printf("lossless iteration %d\n", iteration);
}
// remove vertices & mark deleted triangles
loopi(0, triangles.size())
{
Triangle &t = triangles[i];
if (t.err[3] > threshold)
continue;
if (t.deleted)
continue;
if (t.dirty)
continue;
loopj(0, 3) if (t.err[j] < threshold)
{
int i0 = t.v[j];
Vertex &v0 = vertices[i0];
int i1 = t.v[(j + 1) % 3];
Vertex &v1 = vertices[i1];
// Border check
if (v0.border != v1.border)
continue;
// Compute vertex to collapse to
vec3f p;
calculate_error(i0, i1, p);
deleted0.resize(v0.tcount); // normals temporarily
deleted1.resize(v1.tcount); // normals temporarily
// don't remove if flipped
if (flipped(p, i0, i1, v0, v1, deleted0))
continue;
if (flipped(p, i1, i0, v1, v0, deleted1))
continue;
if ((t.attr & TEXCOORD) == TEXCOORD)
{
update_uvs(i0, v0, p, deleted0);
update_uvs(i0, v1, p, deleted1);
}
// not flipped, so remove edge
v0.p = p;
v0.q = v1.q + v0.q;
int tstart = refs.size();
update_triangles(i0, v0, deleted0, deleted_triangles);
update_triangles(i0, v1, deleted1, deleted_triangles);
int tcount = refs.size() - tstart;
if (tcount <= v0.tcount)
{
// save ram
if (tcount)
memcpy(&refs[v0.tstart], &refs[tstart], tcount * sizeof(Ref));
}
else
// append
v0.tstart = tstart;
v0.tcount = tcount;
break;
}
}
if (deleted_triangles <= 0)
break;
deleted_triangles = 0;
} // for each iteration
// clean up mesh
compact_mesh();
} // simplify_mesh_lossless()
// Check if a triangle flips when this edge is removed
bool flipped(vec3f p, int i0, int i1, Vertex &v0, Vertex &v1, std::vector<int> &deleted)
{
loopk(0, v0.tcount)
{
Triangle &t = triangles[refs[v0.tstart + k].tid];
if (t.deleted)
continue;
int s = refs[v0.tstart + k].tvertex;
int id1 = t.v[(s + 1) % 3];
int id2 = t.v[(s + 2) % 3];
if (id1 == i1 || id2 == i1) // delete ?
{
deleted[k] = 1;
continue;
}
vec3f d1 = vertices[id1].p - p;
d1.normalize();
vec3f d2 = vertices[id2].p - p;
d2.normalize();
if (fabs(d1.dot(d2)) > 0.999)
return true;
vec3f n;
n.cross(d1, d2);
n.normalize();
deleted[k] = 0;
if (n.dot(t.n) < 0.2)
return true;
}
return false;
}
// update_uvs
void update_uvs(int i0, const Vertex &v, const vec3f &p, std::vector<int> &deleted)
{
loopk(0, v.tcount)
{
Ref &r = refs[v.tstart + k];
Triangle &t = triangles[r.tid];
if (t.deleted)
continue;
if (deleted[k])
continue;
vec3f p1 = vertices[t.v[0]].p;
vec3f p2 = vertices[t.v[1]].p;
vec3f p3 = vertices[t.v[2]].p;
t.uvs[r.tvertex] = interpolate(p, p1, p2, p3, t.uvs);
}
}
// Update triangle connections and edge error after a edge is collapsed
void update_triangles(int i0, Vertex &v, std::vector<int> &deleted, int &deleted_triangles)
{
vec3f p;
loopk(0, v.tcount)
{
Ref &r = refs[v.tstart + k];
Triangle &t = triangles[r.tid];
if (t.deleted)
continue;
if (deleted[k])
{
t.deleted = 1;
deleted_triangles++;
continue;
}
t.v[r.tvertex] = i0;
t.dirty = 1;
t.err[0] = calculate_error(t.v[0], t.v[1], p);
t.err[1] = calculate_error(t.v[1], t.v[2], p);
t.err[2] = calculate_error(t.v[2], t.v[0], p);
t.err[3] = min(t.err[0], min(t.err[1], t.err[2]));
refs.push_back(r);
}
}
// compact triangles, compute edge error and build reference list
void update_mesh(int iteration)
{
if (iteration > 0) // compact triangles
{
int dst = 0;
loopi(0, triangles.size()) if (!triangles[i].deleted)
{
triangles[dst++] = triangles[i];
}
triangles.resize(dst);
}
//
// Init Reference ID list
loopi(0, vertices.size())
{
vertices[i].tstart = 0;
vertices[i].tcount = 0;
}
loopi(0, triangles.size())
{
Triangle &t = triangles[i];
loopj(0, 3) vertices[t.v[j]].tcount++;
}
int tstart = 0;
loopi(0, vertices.size())
{
Vertex &v = vertices[i];
v.tstart = tstart;
tstart += v.tcount;
v.tcount = 0;
}
// Write References
refs.resize(triangles.size() * 3);
loopi(0, triangles.size())
{
Triangle &t = triangles[i];
loopj(0, 3)
{
Vertex &v = vertices[t.v[j]];
refs[v.tstart + v.tcount].tid = i;
refs[v.tstart + v.tcount].tvertex = j;
v.tcount++;
}
}
// Init Quadrics by Plane & Edge Errors
//
// required at the beginning ( iteration == 0 )
// recomputing during the simplification is not required,
// but mostly improves the result for closed meshes
//
if (iteration == 0)
{
// Identify boundary : vertices[].border=0,1
std::vector<int> vcount, vids;
loopi(0, vertices.size())
vertices[i]
.border = 0;
loopi(0, vertices.size())
{
Vertex &v = vertices[i];
vcount.clear();
vids.clear();
loopj(0, v.tcount)
{
int k = refs[v.tstart + j].tid;
Triangle &t = triangles[k];
loopk(0, 3)
{
int ofs = 0, id = t.v[k];
while (ofs < vcount.size())
{
if (vids[ofs] == id)
break;
ofs++;
}
if (ofs == vcount.size())
{
vcount.push_back(1);
vids.push_back(id);
}
else
vcount[ofs]++;
}
}
loopj(0, vcount.size()) if (vcount[j] == 1)
vertices[vids[j]]
.border = 1;
}
// initialize errors
loopi(0, vertices.size())
vertices[i]
.q = SymetricMatrix(0.0);
loopi(0, triangles.size())
{
Triangle &t = triangles[i];
vec3f n, p[3];
loopj(0, 3) p[j] = vertices[t.v[j]].p;
n.cross(p[1] - p[0], p[2] - p[0]);
n.normalize();
t.n = n;
loopj(0, 3) vertices[t.v[j]].q =
vertices[t.v[j]].q + SymetricMatrix(n.x, n.y, n.z, -n.dot(p[0]));
}
loopi(0, triangles.size())
{
// Calc Edge Error
Triangle &t = triangles[i];
vec3f p;
loopj(0, 3) t.err[j] = calculate_error(t.v[j], t.v[(j + 1) % 3], p);
t.err[3] = min(t.err[0], min(t.err[1], t.err[2]));
}
}
}
// Finally compact mesh before exiting
void compact_mesh()
{
int dst = 0;
loopi(0, vertices.size())
{
vertices[i].tcount = 0;
}
loopi(0, triangles.size()) if (!triangles[i].deleted)
{
Triangle &t = triangles[i];
triangles[dst++] = t;
loopj(0, 3) vertices[t.v[j]].tcount = 1;
}
triangles.resize(dst);
dst = 0;
loopi(0, vertices.size()) if (vertices[i].tcount)
{
vertices[i].tstart = dst;
vertices[dst].p = vertices[i].p;
dst++;
}
loopi(0, triangles.size())
{
Triangle &t = triangles[i];
loopj(0, 3) t.v[j] = vertices[t.v[j]].tstart;
}
vertices.resize(dst);
}
// Error between vertex and Quadric
double vertex_error(SymetricMatrix q, double x, double y, double z)
{
return q[0] * x * x + 2 * q[1] * x * y + 2 * q[2] * x * z + 2 * q[3] * x + q[4] * y * y + 2 * q[5] * y * z + 2 * q[6] * y + q[7] * z * z + 2 * q[8] * z + q[9];
}
// Error for one edge
double calculate_error(int id_v1, int id_v2, vec3f &p_result)
{
// compute interpolated vertex
SymetricMatrix q = vertices[id_v1].q + vertices[id_v2].q;
bool border = vertices[id_v1].border & vertices[id_v2].border;
double error = 0;
double det = q.det(0, 1, 2, 1, 4, 5, 2, 5, 7);
if (det != 0 && !border)
{
// q_delta is invertible
p_result.x = -1 / det * (q.det(1, 2, 3, 4, 5, 6, 5, 7, 8)); // vx = A41/det(q_delta)
p_result.y = 1 / det * (q.det(0, 2, 3, 1, 5, 6, 2, 7, 8)); // vy = A42/det(q_delta)
p_result.z = -1 / det * (q.det(0, 1, 3, 1, 4, 6, 2, 5, 8)); // vz = A43/det(q_delta)
error = vertex_error(q, p_result.x, p_result.y, p_result.z);
}
else
{
// det = 0 -> try to find best result
vec3f p1 = vertices[id_v1].p;
vec3f p2 = vertices[id_v2].p;
vec3f p3 = (p1 + p2) / 2;
double error1 = vertex_error(q, p1.x, p1.y, p1.z);
double error2 = vertex_error(q, p2.x, p2.y, p2.z);
double error3 = vertex_error(q, p3.x, p3.y, p3.z);
error = min(error1, min(error2, error3));
if (error1 == error)
p_result = p1;
if (error2 == error)
p_result = p2;
if (error3 == error)
p_result = p3;
}
return error;
}
char *trimwhitespace(char *str)
{
char *end;
// Trim leading space
while (isspace((unsigned char)*str))
str++;
if (*str == 0) // All spaces?
return str;
// Trim trailing space
end = str + strlen(str) - 1;
while (end > str && isspace((unsigned char)*end))
end--;
// Write new null terminator
*(end + 1) = 0;
return str;
}
// Option : Load OBJ
void load_obj(const char *filename, bool process_uv = false)
{
vertices.clear();
triangles.clear();
// printf ( "Loading Objects %s ... \n",filename);
FILE *fn;
if (filename == NULL)
return;
if ((char)filename[0] == 0)
return;
if ((fn = fopen(filename, "rb")) == NULL)
{
printf("File %s not found!\n", filename);
return;
}
char line[1000];
memset(line, 0, 1000);
int vertex_cnt = 0;
int material = -1;
std::map<std::string, int> material_map;
std::vector<vec3f> uvs;
std::vector<std::vector<int>> uvMap;
while (fgets(line, 1000, fn) != NULL)
{
Vertex v;
vec3f uv;
if (strncmp(line, "mtllib", 6) == 0)
{
mtllib = trimwhitespace(&line[7]);
}
if (strncmp(line, "usemtl", 6) == 0)
{
std::string usemtl = trimwhitespace(&line[7]);
if (material_map.find(usemtl) == material_map.end())
{
material_map[usemtl] = materials.size();
materials.push_back(usemtl);
}