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ntcd.h
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ntcd.h
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// LICENSE
//
// MIT License
//
// Copyright (c) 2017 Nikos Tasios
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//
//
// USAGE
//
// Include this file in whatever places neeed to refer to it. In ONE C/C++
// file, write:
// #define STB_TRUETYPE_IMPLEMENTATION
// before the #include of this file. This expands out the actual
// implementation into that C/C++ file.
//
// To make the implementation private to the file that generates the implementation,
// #define STBTT_STATIC
//
// DOCUMENTATION
//
// Please read the comments in the 'Interface' section for documentation.
// Below you can find a usage example. The example can be copied to a separate
// file and compiled.
//
#if 0
#define NTCD_IMPLEMENTATION
#include "ntcd.h"
#include <math.h>
#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950288
#endif
#include <assert.h>
int main(int argc, char* argv[]){
ntcd_cylinder cyl;
ntcd_cylinder_initialize(&cyl, 1.0, 1.0);
//Two cylinders of height 1, rotate by 45 degrees around the z-axis,
//should overlap at x = 1 / sin(45).
double d = 1.0 / sin(M_PI / 4.0);
ntcd_transform ta = {
{0.0, 0.0, 0.0},
{0.0, 0.0, sin(M_PI / 8.0), cos(M_PI / 8.0)},
1.0
};
ntcd_transform tb = {
{d - 0.01, 0.0, 0.0},
{0.0, 0.0, sin(M_PI / 8.0), cos(M_PI / 8.0)},
1.0
};
ntcd_transform tc = {
{d + 0.01, 0.0, 0.0},
{0.0, 0.0, sin(M_PI / 8.0), cos(M_PI / 8.0)},
1.0
};
int overlap_a = ntcd_gjk_boolean(&ta, &cyl, &tb, &cyl);
int overlap_b = ntcd_gjk_boolean(&ta, &cyl, &tc, &cyl);
assert(overlap_a != overlap_b);
double dist[3];
ntcd_gjk_distance(dist, &ta, &cyl, &tc, &cyl);
double length = sqrt(dist[0] * dist[0] + dist[1] * dist[1] + dist[2] * dist[2]);
assert(length < 0.01);
assert(length > 0.0);
return 0;
}
#endif
#ifdef NTCD_IMPLEMENTATION
#ifndef NTCD_GJK_ERROR_TOLERANCE
#include <float.h>
#define NTCD_GJK_ERROR_TOLERANCE 10.0 * DBL_EPSILON
#endif
#ifndef NTCD_GJK_RELATIVE_ERROR
#define NTCD_GJK_RELATIVE_ERROR 1.0e-4
#define NTCD_GJK_RELATIVE_ERROR2 NTCD_GJK_RELATIVE_ERROR * NTCD_GJK_RELATIVE_ERROR
#endif
#endif
//Interface (Read this part for documentation)
#ifndef __NTCD_H__
#define __NTCD_H__
#ifdef NTCD_STATIC
#define NTCD_DEF static
#else
#define NTCD_DEF extern
#endif
#ifdef __cplusplus
extern "C"{
#endif
//Shape transform, consisting of the 3d position, the rotation in the form
//of a quaternion, and the size, which scales the shape size. The struct
//should be easy to replace with your own.
typedef struct{
double pos[3];
double rot[4]; //Quaternion
double size;
}ntcd_transform;
//Type of the support function which GJK uses.
typedef void (*ntcd_support)(double*, const void*, const double*);
//Check if two shapes, ca and cb with transforms ta and tb respectively
//overlap. Returns 1 if they overlap and 0 otherwise.
NTCD_DEF int ntcd_gjk_boolean(
const ntcd_transform* ta, const void* ca,
const ntcd_transform* tb, const void* cb
);
//Calculate the closest distance dist_vec between two shapes, ca and cb with
//transforms ta and tb respectively.
NTCD_DEF void ntcd_gjk_distance(
double* dist_vec,
const ntcd_transform* ta, const void* ca,
const ntcd_transform* tb, const void* cb
);
//Calculate the closest points, point_on_a and point_on_b on shape, ca and cb
//with transforms ta and tb respectively. The two outputs are zeroed in case
//the two shapes overlap.
NTCD_DEF void ntcd_gjk_closest_points(
double* point_on_a, double* point_on_b,
const ntcd_transform* ta, const void* ca,
const ntcd_transform* tb, const void* cb
);
//Calculate the distance shape ca with transform ta can be moved on a straight
//line in the direction ray_dir before it meets shape cb with transform tb.
//Returns 0 when shape ca does not meet cb, othewise it returns 1 if it succeeds.
NTCD_DEF int ntcd_gjk_raycast(
double* distance, double* normal,
const ntcd_transform* ta, const void* ca,
const ntcd_transform* tb, const void* cb,
const double* ray_dir
);
//Shapes
//NOTE: Be sure you know how each shape is originally oriented.
//Current supported shapes:
//
// Sphere, Point, Line, Mesh, Cylinder, Box, Cone, Bicone,
// Leaf Cylinder, Sphere-swept, Hull, Minkowski
//Sphere
//The sphere is of radius 1.
typedef struct{
ntcd_support support;
}ntcd_sphere;
NTCD_DEF void ntcd_sphere_initialize(ntcd_sphere* sph);
//Point
typedef struct{
ntcd_support support;
}ntcd_point;
NTCD_DEF void ntcd_point_initialize(ntcd_point* point);
//Line
//The line is of length 1 and is parallel to the y-axis.
typedef struct{
ntcd_support support;
}ntcd_line;
NTCD_DEF void ntcd_line_initialize(ntcd_line* line);
//Disk
//The disk is of radius 1 and its axis is parallel to the y-axis.
typedef struct{
ntcd_support support;
}ntcd_disk;
NTCD_DEF void ntcd_disk_initialize(ntcd_disk* disk);
//Mesh
typedef struct{
ntcd_support support;
unsigned int n_vertices_;
double* vertices_;
unsigned int* n_vert_neighbours_;
unsigned int** vert_neighbours_;
}ntcd_mesh;
//Initializing a mesh is slightly involved. The mesh vertices and the vertex
//indices of each face need to be passed. The vertices are passed as a flat array
//of size 3 * n_vertices. Vertex i with i < n_vertices is given by (vertices + 3 * i).
//The vertex indices of each face are also passed as a flat array. The array face_start
//stores the array position inside faces where each face starts.
//
//As an example, suppose we would like to load a tetrahedron with edge length 2. The
//4 vertices are located at,
//
// { 1, 0, -1 / sqrt(2)},
// {-1, 0, -1 / sqrt(2)},
// { 0, 1, 1 / sqrt(2)},
// { 0, -1, 1 / sqrt(2)}
//
//The four faces are defined as (note that the order of face indices does not play
//any role in our mesh implementation),
//
// {0, 1, 2},
// {0, 1, 3},
// {0, 2, 3},
// {1, 2, 3}
//
//The vertices array passed would then look like,
//
// vertices[] = {
// 1, 0, -1 / sqrt(2), -1, 0, -1 / sqrt(2),
// 0, 1, 1 / sqrt(2), 0, -1, 1 / sqrt(2)
// }
//
//while faces would look like,
//
// faces[] = {0, 1, 2, 0, 1, 3, 0, 2, 3, 1, 2, 3}
//
//and face_start,
//
// face_start[] = {0, 3, 6, 9}
//
//Also note that faces are not required to have 3 vertices, and that different faces
//of the shame shape need not have the same number of vertices either.
NTCD_DEF void ntcd_mesh_initialize(
ntcd_mesh* mesh,
const unsigned int n_vertices, const double* vertices,
const unsigned int n_faces, const unsigned int* face_start, const unsigned int* faces
);
NTCD_DEF void ntcd_mesh_terminate(ntcd_mesh* mesh);
//Cylinder
//The cylinder is of radius base_radius and height height, and its axis of symmetry is
//parallel to the y-axis.
typedef struct{
ntcd_support support;
double base_radius_, half_height_;
}ntcd_cylinder;
NTCD_DEF void ntcd_cylinder_initialize(ntcd_cylinder* cyl, double base_radius, double height);
//Box
//The length of each side of the box is give by the extent array.
typedef struct{
ntcd_support support;
double extent_[3];
}ntcd_box;
NTCD_DEF void ntcd_box_initialize(ntcd_box* box, const double* extent);
//Cone
//The cone has a base radius base_radius and height height, and its axis of symmetry is
//parallel to the y-axis.
typedef struct{
ntcd_support support;
double base_radius_, half_height_;
double sintheta_;
}ntcd_cone;
NTCD_DEF void ntcd_cone_initialize(ntcd_cone* cone, double base_radius, double height);
//Bicone
//The bicone has a mid radius base_radius and height height, and its axis of symmetry is
//parallel to the y-axis.
typedef struct{
ntcd_support support;
double base_radius_, half_height_;
double sintheta_;
}ntcd_bicone;
NTCD_DEF void ntcd_bicone_initialize(ntcd_bicone* bicone, double base_radius, double height);
//Leaf Cylinder
typedef struct{
ntcd_support support;
double half_width_, half_length_, half_height_;
double circle_radius_, circle_distance_;
}ntcd_leaf_cylinder;
NTCD_DEF void ntcd_leaf_cylinder_initialize(ntcd_leaf_cylinder* leaf, double width, double length, double height);
//Sphere-swept
//The sphere swept shape is produced from a shape, by sweeping a sphere around the
//shape's surface.
typedef struct{
ntcd_support support;
const void* shape_;
double radius_;
}ntcd_sphere_swept;
NTCD_DEF void ntcd_sphere_swept_initialize(ntcd_sphere_swept* msum, double radius, const void* shape);
//Hull
//The convex hull of two shapes.
typedef struct{
ntcd_support support;
const void* ca_;
const void* cb_;
ntcd_transform ta_;
ntcd_transform tb_;
//Cache inverse rotations.
double inv_rot_a_[4];
double inv_rot_b_[4];
}ntcd_hull;
NTCD_DEF void ntcd_hull_initialize(ntcd_hull* hull, const ntcd_transform* ta, const void* ca, const ntcd_transform* tb, const void* cb);
//Minkowski
//The minkowski sum of two shapes. The transform t is applied to the second shape, cb.
typedef struct{
ntcd_support support;
const void* ca_;
const void* cb_;
ntcd_transform t_;
//Cache inverse rotation.
double inv_rot_[4];
}ntcd_minkowski_sum;
NTCD_DEF void ntcd_minkowski_sum_initialize(ntcd_minkowski_sum* msum, const ntcd_transform* t, const void* ca, const void* cb);
#ifdef __cplusplus
}
#endif
#endif //__NTCD_H__
//Implementation
#ifdef NTCD_IMPLEMENTATION
//TODO: Investigate raycast false positives on y-axis for cylinders.
//TODO: Impelement EPA for penetration depth.
//TODO: Implement Johnson's dstance algorithm as an alternative.
//TODO: Add MPR?
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include <float.h>
#define BARY_GEPP
//Vectors
static double ntcd__vec3_dot(const double* a, const double* b){
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
static void ntcd__vec3_cross(double* c, const double* a, const double* b){
c[0] = a[1] * b[2] - a[2] * b[1];
c[1] = a[2] * b[0] - a[0] * b[2];
c[2] = a[0] * b[1] - a[1] * b[0];
}
//Calculates d = (a x b) x c
static void ntcd__vec3_triple_product(double* d, const double* a, const double* b, const double* c){
d[0] = b[0] * ntcd__vec3_dot(a, c) - a[0] * ntcd__vec3_dot(b, c);
d[1] = b[1] * ntcd__vec3_dot(a, c) - a[1] * ntcd__vec3_dot(b, c);
d[2] = b[2] * ntcd__vec3_dot(a, c) - a[2] * ntcd__vec3_dot(b, c);
}
static void ntcd__vec3_add(double*c, const double* a, const double* b){
c[0] = a[0] + b[0];
c[1] = a[1] + b[1];
c[2] = a[2] + b[2];
}
static void ntcd__vec3_sub(double* c, const double* a, const double* b){
c[0] = a[0] - b[0];
c[1] = a[1] - b[1];
c[2] = a[2] - b[2];
}
static void ntcd__vec3_smul(double* c, double f, const double* a){
c[0] = f * a[0];
c[1] = f * a[1];
c[2] = f * a[2];
}
static void ntcd__vec3_fmadd(double* c, double a, const double* x, const double* y){
c[0] = a * x[0] + y[0];
c[1] = a * x[1] + y[1];
c[2] = a * x[2] + y[2];
}
static double ntcd__vec3_length2(const double* vec){
return vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2];
}
static double ntcd__vec3_length(const double* vec){
return sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]);
}
//TODO: Try memcmp performance
static int ntcd__vec3_equal(const double* a, const double* b){
return (a[0] == b[0]) && (a[1] == b[1]) && (a[2] == b[2]);
}
// Quaternions
//TODO: Do we really need to calculate the length? Aren't all quaternions assumed of unit length?
static void ntcd__quat_inverse(double* r, const double* q){
double ilength2 = 1.0 / (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
r[0] = -q[0] * ilength2;
r[1] = -q[1] * ilength2;
r[2] = -q[2] * ilength2;
r[3] = q[3] * ilength2;
}
static void ntcd__quat_vec3_rotate(double* r, const double* q, const double* v){
double u[3];
{
double a[3], b[3];
ntcd__vec3_cross(a, q, v);
ntcd__vec3_fmadd(b, q[3], v, a);
ntcd__vec3_cross(u, q, b);
}
ntcd__vec3_fmadd(r, 2.0, u, v);
//TODO: Check if this is faster
//r[0] = v[0] + 2.0 * (q[1] * (q[0] * v[1] - q[1] * v[0] + q[3] * v[2]) - q[2] * (q[2] * v[0] - q[0] * v[2] + q[3] * v[1]));
//r[1] = v[1] + 2.0 * (q[2] * (q[1] * v[2] - q[2] * v[1] + q[3] * v[0]) - q[0] * (q[0] * v[1] - q[1] * v[0] + q[3] * v[2]));
//r[2] = v[2] + 2.0 * (q[0] * (q[2] * v[0] - q[0] * v[2] + q[3] * v[1]) - q[1] * (q[1] * v[2] - q[2] * v[1] + q[3] * v[0]));
}
//Lookup table for single enabled bit position -- Calculates the log2 of a 4-bit integer.
static const unsigned char s_pos[] = {0, 0, 1, 0, 2, 0, 0, 0, 3};
//_______________________________________^__^_____^___________^
//Lookup table which tells us at which positions in the simplex array
//to get our points a, b, c, d. I.e. if our bits are 0111 -> 7 -> {0, 1, 2}
static const unsigned char p_pos[16][3] =
{
{0, 0, 0}, {0, 0, 0}, {1, 0, 0}, {0, 1, 0},
{2, 0, 0}, {0, 2, 0}, {1, 2, 0}, {0, 1, 2},
{3, 0, 0}, {0, 3, 0}, {1, 3, 0}, {0, 1, 3},
{2, 3, 0}, {0, 2, 3}, {1, 2, 3}, {0, 0, 0}
};
#if defined(BARY_ERICSON)
static double triangle_area_2D(double x1, double y1, double x2, double y2, double x3, double y3){
return (x1 - x2) * (y2 - y3) - (x2 - x3) * (y1 - y2);
}
//Algorithm for calculating barycentric coordinates from
//'Real-time collision detection' by Christer Ericson.
static void barycentric_coordinates(double* R, const double* P, const double* A, const double* B, const double* C){
double u, v, w;
double m[3];
{
double AB[3], AC[3];
ntcd__vec3_sub(AB, B, A);
ntcd__vec3_sub(AC, C, A);
ntcd__vec3_cross(m, AB, AC);
}
double nu, nv, ood;
double x = fabs(m[0]), y = fabs(m[1]), z = fabs(m[2]);
if(x >= y && x >= z){
nu = triangle_area_2D(P[1], P[2], B[1], B[2], C[1], C[2]);
nv = triangle_area_2D(P[1], P[2], C[1], C[2], A[1], A[2]);
ood = 1.0 / m[0];
}
else if(y >= x && y >= z){
nu = triangle_area_2D(P[0], P[2], B[0], B[2], C[0], C[2]);
nv = triangle_area_2D(P[0], P[2], C[0], C[2], A[0], A[2]);
ood = 1.0 / -m[1];
}
else{
nu = triangle_area_2D(P[0], P[1], B[0], B[1], C[0], C[1]);
nv = triangle_area_2D(P[0], P[1], C[0], C[1], A[0], A[1]);
ood = 1.0 / m[2];
}
R[0] = nu * ood;
R[1] = nv * ood;
R[2] = 1.0 - R[0] - R[1];
}
#elif defined(BARY_CRAMER)
static void barycentric_coordinates(double* R, const double* P, const double* A, const double* B, const double* C){
double v0[3], v1[3], v2[3];
ntcd__vec3_sub(v0, B, A);
ntcd__vec3_sub(v1, C, A);
ntcd__vec3_sub(v2, P, A);
double d00 = ntcd__vec3_dot(v0, v0);
double d01 = ntcd__vec3_dot(v0, v1);
double d02 = ntcd__vec3_dot(v0, v2);
double d11 = ntcd__vec3_dot(v1, v1);
double d12 = ntcd__vec3_dot(v1, v2);
double denom = d00 * d11 - d01 * d01;
R[0] = (d11 * d02 - d01 * d12) / denom;
R[1] = (d00 * d12 - d01 * d02) / denom;
R[2] = 1.0 - R[0] - R[1];
}
#elif defined(BARY_GEPP)
static void barycentric_coordinates(double* R, const double* P, const double* A, const double* B, const double* C){
double v0[3], v1[3], v2[3];
ntcd__vec3_sub(v0, B, A);
ntcd__vec3_sub(v1, C, A);
ntcd__vec3_sub(v2, P, A);
double d00 = ntcd__vec3_dot(v0, v0);
double d01 = ntcd__vec3_dot(v0, v1);
double d02 = ntcd__vec3_dot(v0, v2);
double d11 = ntcd__vec3_dot(v1, v1);
double d12 = ntcd__vec3_dot(v1, v2);
R[0] = (d00 * d12 - d01 * d02) / (d00 * d11 - d01 * d01);
R[1] = (d00 >= d01)? (d02 - d01 * R[0]) / d00: (d12 - d11 * R[0]) / d01;
//R[1] = (d00 >= d01)? d02 / d00 - (d01 / d00) * w: d12 / d01 - (d11 / d01) * w;
R[2] = 1.0 - R[0] - R[1];
}
#endif
typedef struct{
unsigned char bits_;
unsigned char last_sb_;
unsigned char size_;
double p_[3 * 4];
double a_[3 * 4];
double b_[3 * 4];
double max_vert2_;
}ntcd__simplex;
static void ntcd__simplex_initialize(ntcd__simplex* simplex){
simplex->bits_ = 0;
simplex->last_sb_ = 0;
simplex->size_ = 0;
simplex->max_vert2_ = 0.0;
}
//void ntcd__simplex_print(const ntcd__simplex* simplex){
// printf("yo\n");
// unsigned char bits = simplex->bits_;
// for(int i = 0; i < 4; ++i, bits >>= 1){
// if(bits & 1) printf("%d: %f, %f, %f\n", i, simplex->p_[3 * i + 0], simplex->p_[3 * i + 1], simplex->p_[3 * i + 2]);
// }
//}
static void ntcd__simplex_add_point(ntcd__simplex* simplex, const double* point){
unsigned char b = ~simplex->bits_; //Flip bits
b &= -b; //Last set (available) bit
unsigned char pos = s_pos[b]; //Get the bit position from the lookup table
simplex->last_sb_ = pos;
simplex->bits_ |= b; //Insert the new bit
++simplex->size_;
memcpy(simplex->p_ + 3 * pos, point, 3 * sizeof(*point));
double l2 = ntcd__vec3_length2(point);
if(l2 > simplex->max_vert2_) simplex->max_vert2_ = l2;
}
static void ntcd__simplex_add_point_with_info(ntcd__simplex* simplex, const double* point, const double* pa, const double* pb){
ntcd__simplex_add_point(simplex, point);
memcpy(simplex->a_ + 3 * simplex->last_sb_, pa, 3 * sizeof(*pa));
memcpy(simplex->b_ + 3 * simplex->last_sb_, pb, 3 * sizeof(*pb));
}
static void ntcd__simplex_remove_point(ntcd__simplex* simplex, int p){
simplex->bits_ ^= (1 << p); //Erase the bit at position p
--simplex->size_;
}
static int ntcd__simplex_contains(const ntcd__simplex* simplex, const double* point){
unsigned char bits = simplex->bits_;
for(int i = 0; i < 4; ++i, bits >>= 1){
if((bits & 1) && ntcd__vec3_equal(simplex->p_ + 3 * i, point)) return 1;
}
return 0;
}
static void ntcd__simplex_translate(ntcd__simplex* simplex, const double* dr){
//for(int k = 0; k < 4; ++k) p_[k] += dr;
simplex->max_vert2_ = 0.0;
unsigned char bits = simplex->bits_;
for(int i = 0; i < 4; ++i, bits >>= 1){
if(bits & 1){
ntcd__vec3_add(simplex->p_ + 3 * i, dr, simplex->p_ + 3 * i);
if(ntcd__vec3_length2(simplex->p_ + 3 * i) > simplex->max_vert2_) simplex->max_vert2_ = ntcd__vec3_length2(simplex->p_ + 3 * i);
}
}
}
static void ntcd__simplex_compute_closest_points(ntcd__simplex* simplex, double* pa, double* pb, const double* P){
switch(simplex->size_){
//IMPORTANT: We are having accuracy problems with this projection.
case 3:{
const unsigned char* pos = p_pos[(simplex->bits_ ^ (1 << simplex->last_sb_))];
const double* aA = simplex->a_ + 3 * simplex->last_sb_;
const double* aB = simplex->a_ + 3 * pos[0];
const double* aC = simplex->a_ + 3 * pos[1];
const double* bA = simplex->b_ + 3 * simplex->last_sb_;
const double* bB = simplex->b_ + 3 * pos[0];
const double* bC = simplex->b_ + 3 * pos[1];
const double* A = simplex->p_ + 3 * simplex->last_sb_;
const double* B = simplex->p_ + 3 * pos[0];
const double* C = simplex->p_ + 3 * pos[1];
double bary[3];
barycentric_coordinates(bary, P, A, B, C);
for(int i = 0; i < 3; ++i){
pa[i] = aA[i] * bary[0] + aB[i] * bary[1] + aC[i] * bary[2];
pb[i] = bA[i] * bary[0] + bB[i] * bary[1] + bC[i] * bary[2];
}
break;
}
case 2:{
const unsigned char* pos = p_pos[(simplex->bits_ ^ (1 << simplex->last_sb_))];
const double* aA = simplex->a_ + 3 * simplex->last_sb_;
const double* aB = simplex->a_ + 3 * pos[0];
const double* bA = simplex->b_ + 3 * simplex->last_sb_;
const double* bB = simplex->b_ + 3 * pos[0];
double u, v;
{
const double* A = simplex->p_ + 3 * simplex->last_sb_;
const double* B = simplex->p_ + 3 * pos[0];
{
double AB[3], AP[3];
ntcd__vec3_sub(AB, B, A);
ntcd__vec3_sub(AP, P, A);
v = ntcd__vec3_dot(AB, AP) / ntcd__vec3_length2(AB);
u = 1.0 - v;
}
}
for(int i = 0; i < 3; ++i){
pa[i] = aA[i] * u + aB[i] * v;
pb[i] = bA[i] * u + bB[i] * v;
}
break;
}
case 1:{
memcpy(pa, simplex->a_ + 3 * simplex->last_sb_, 3 * sizeof(*pa));
memcpy(pb, simplex->b_ + 3 * simplex->last_sb_, 3 * sizeof(*pb));
break;
}
default:
break;
}
}
//Reduce the simple to its feature closest to the origin and update the search direction, dir.
static void ntcd__simplex_closest(ntcd__simplex* simplex, double* dir){
switch(simplex->size_){
case 4:
{
const unsigned char* pos = p_pos[(simplex->bits_ ^ (1 << simplex->last_sb_))];
const double* a = simplex->p_ + 3 * simplex->last_sb_;
const double* b = simplex->p_ + 3 * pos[0];
const double* c = simplex->p_ + 3 * pos[1];
const double* d = simplex->p_ + 3 * pos[2];
double ab[3], ac[3], ad[3];
ntcd__vec3_sub(ab, b, a);
ntcd__vec3_sub(ac, c, a);
ntcd__vec3_sub(ad, d, a);
////////////////////* Vertex Case *///////////////////
double dot_aba = ntcd__vec3_dot(ab, a);
double dot_aca = ntcd__vec3_dot(ac, a);
double dot_ada = ntcd__vec3_dot(ad, a);
if(dot_aba >= 0.0 && dot_aca >= 0.0 && dot_ada >= 0.0){
memcpy(dir, a, 3 * sizeof(*dir)); //Take direction passing through origin
ntcd__simplex_remove_point(simplex, pos[0]);
ntcd__simplex_remove_point(simplex, pos[1]);
ntcd__simplex_remove_point(simplex, pos[2]);
break;
}
////////////////////* Edge Cases *///////////////////
/* ab Edge case */
double dot_abb = ntcd__vec3_dot(ab, b);
double dot_abPerp1 = dot_aba * ntcd__vec3_dot(ac, b) - dot_abb * dot_aca;
double dot_abPerp2 = dot_aba * ntcd__vec3_dot(ad, b) - dot_abb * dot_ada;
// The origin must be inside the space defined by the intersection
// of two half-space normal to the adjacent faces abc, abd
if(dot_abPerp1 <= 0.0 && dot_abPerp2 <= 0.0 && dot_aba <= 0.0){
double f = dot_aba / (dot_aba - dot_abb);
ntcd__vec3_fmadd(dir, f, ab, a);
ntcd__simplex_remove_point(simplex, pos[1]);
ntcd__simplex_remove_point(simplex, pos[2]);
break;
}
/* ac Edge case */
double dot_acc = ntcd__vec3_dot(ac, c);
double dot_acPerp1 = dot_aca * ntcd__vec3_dot(ad, c) - dot_acc * dot_ada;
double dot_acPerp2 = dot_aca * ntcd__vec3_dot(ab, c) - dot_acc * dot_aba;
// The origin must be inside the space defined by the intersection
// of two half-space normal to the adjacent faces abc, acd
if(dot_acPerp1 <= 0.0 && dot_acPerp2 <= 0.0 && dot_aca <= 0.0){
double f = dot_aca / (dot_aca - dot_acc);
ntcd__vec3_fmadd(dir, f, ac, a);
ntcd__simplex_remove_point(simplex, pos[0]);
ntcd__simplex_remove_point(simplex, pos[2]);
break;
}
/* ad Edge case */
double dot_add = ntcd__vec3_dot(ad, d);
double dot_adPerp1 = dot_ada * ntcd__vec3_dot(ab, d) - dot_add * dot_aba;
double dot_adPerp2 = dot_ada * ntcd__vec3_dot(ac, d) - dot_add * dot_aca;
// The origin must be inside the space defined by the intersection
// of two half-space normal to the adjacent faces acd, abd
if(dot_adPerp1 <= 0.0 && dot_adPerp2 <= 0.0 && dot_ada <= 0.0){
double f = dot_ada / (dot_ada - dot_add);
ntcd__vec3_fmadd(dir, f, ad, a);
ntcd__simplex_remove_point(simplex, pos[0]);
ntcd__simplex_remove_point(simplex, pos[1]);
break;
}
////////////////////* Face Cases *///////////////////
/* On abc side */
// The origin should be on abc's side and between the half-spaces defined by ac and ab (normal to abc)
{
double abxac[3];
ntcd__vec3_cross(abxac, ab, ac);
if(ntcd__vec3_dot(ad, abxac) * ntcd__vec3_dot(a, abxac) > 0.0 && dot_abPerp1 >= 0.0 && dot_acPerp2 >= 0.0){
/* Remove point d */
ntcd__simplex_remove_point(simplex, pos[2]);
ntcd__vec3_smul(dir, ntcd__vec3_dot(abxac, a) / ntcd__vec3_length2(abxac), abxac);
break;
}
}
/* On abd side */
// The origin should be on abd's side and between the half-spaces defined by ab and ad (normal to abd)
{
double abxad[3];
ntcd__vec3_cross(abxad, ab, ad);
if(ntcd__vec3_dot(ac, abxad) * ntcd__vec3_dot(a, abxad) > 0.0 && dot_abPerp2 >= 0.0 && dot_adPerp1 >= 0.0){
/* Remove point c */
ntcd__simplex_remove_point(simplex, pos[1]);
ntcd__vec3_smul(dir, ntcd__vec3_dot(abxad, a) / ntcd__vec3_length2(abxad), abxad);
break;
}
}
///* On acd side */
// The origin should be on acd's side and between the half-spaces defined by ac and ad (normal to acd)
{
double acxad[3];
ntcd__vec3_cross(acxad, ac, ad);
if(ntcd__vec3_dot(ab, acxad) * ntcd__vec3_dot(a, acxad) > 0.0 && dot_acPerp1 >= 0.0 && dot_adPerp2 >= 0.0){
/* Remove point b */
ntcd__simplex_remove_point(simplex, pos[0]);
ntcd__vec3_smul(dir, ntcd__vec3_dot(acxad, a) / ntcd__vec3_length2(acxad), acxad);
break;
}
}
///* On bcd side */
//// The origin should be on bcd's side
{
double bc[3], bd[3], bcxbd[3];
ntcd__vec3_sub(bc, c, b);
ntcd__vec3_sub(bd, d, b);
ntcd__vec3_cross(bcxbd, bc, bd);
if(ntcd__vec3_dot(bcxbd, ab) * ntcd__vec3_dot(bcxbd, b) < 0.0){
/* Remove point a */
ntcd__simplex_remove_point(simplex, simplex->last_sb_);
simplex->last_sb_ = pos[0];
ntcd__vec3_smul(dir, ntcd__vec3_dot(bcxbd, b) / ntcd__vec3_length2(bcxbd), bcxbd);
break;
}
}
/* 'else' should only be when the origin is inside the tetrahedron */
break;
}
case 3:
{
const unsigned char* pos = p_pos[(simplex->bits_ ^ (1 << simplex->last_sb_))];
const double* a = simplex->p_ + 3 * simplex->last_sb_;
const double* b = simplex->p_ + 3 * pos[0];
const double* c = simplex->p_ + 3 * pos[1];
double ab[3], ac[3];
ntcd__vec3_sub(ab, b, a);
ntcd__vec3_sub(ac, c, a);
// Check if O in vertex region A
double dot_aba = -ntcd__vec3_dot(ab, a);
double dot_aca = -ntcd__vec3_dot(ac, a);
if(dot_aba <= 0.0 && dot_aca <= 0.0){
memcpy(dir, a, 3 * sizeof(*dir)); //Take direction passing through origin
ntcd__simplex_remove_point(simplex, pos[0]);
ntcd__simplex_remove_point(simplex, pos[1]);
break;
}
// Check if O in edge region AB
double dot_abb = -ntcd__vec3_dot(ab, b);
double dot_acb = -ntcd__vec3_dot(ac, b);
double vc = dot_aba * dot_acb - dot_abb * dot_aca;
if(vc <= 0.0 && dot_aba >= 0.0 && dot_abb <= 0.0){
double f = dot_aba / (dot_aba - dot_abb);
ntcd__vec3_fmadd(dir, f, ab, a);
/* Remove Point c */
ntcd__simplex_remove_point(simplex, pos[1]);
break;
}
// Check if O in edge region AC
double dot_abc = -ntcd__vec3_dot(ab, c);
double dot_acc = -ntcd__vec3_dot(ac, c);
double vb = dot_abc * dot_aca - dot_aba * dot_acc;
if(vb <= 0.0 && dot_aca >= 0.0 && dot_acc <= 0.0){
double f = dot_aca / (dot_aca - dot_acc);
ntcd__vec3_fmadd(dir, f, ac, a);
/* Remove Point b */
ntcd__simplex_remove_point(simplex, pos[0]);
break;
}
double va = dot_abb * dot_acc - dot_abc * dot_acb;
double w = 1.0 / (va + vb + vc);
for(int i = 0; i < 3; ++i) dir[i] = a[i] + (ab[i] * vb + ac[i] * vc) * w;
break;
}
case 2:
{
const unsigned char* pos = p_pos[(simplex->bits_ ^ (1 << simplex->last_sb_))];
const double* a = simplex->p_ + 3 * simplex->last_sb_;
const double* b = simplex->p_ + 3 * pos[0];
double ab[3];
ntcd__vec3_sub(ab, b, a);
double t = -ntcd__vec3_dot(ab, a);
if(t <= 0.0){
memcpy(dir, a, 3 * sizeof(*dir)); //Take direction passing through origin
ntcd__simplex_remove_point(simplex, pos[0]);
break;
}
double denom = ntcd__vec3_length2(ab);
if(t >= denom){
ntcd__simplex_remove_point(simplex, simplex->last_sb_);
simplex->last_sb_ = pos[0];
memcpy(dir, b, 3 * sizeof(*dir));
break;
}
ntcd__vec3_fmadd(dir, t / denom, ab, a);
break;
}
case 1:
{
memcpy(dir, simplex->p_ + 3 * simplex->last_sb_, 3 * sizeof(*dir));
break;
}
default: break;
}
}
//TODO: dir -> -dir
//Check if the origin is contained in the simplex and update the search direction, dir.
static int ntcd__simplex_contains_origin(ntcd__simplex* simplex, double* dir){
///////////////////////////////////////////////
switch(simplex->size_){
case 4:
{
const unsigned char* pos = p_pos[(simplex->bits_ ^ (1 << simplex->last_sb_))];
const double* a = simplex->p_ + 3 * simplex->last_sb_;
const double* b = simplex->p_ + 3 * pos[0];
const double* c = simplex->p_ + 3 * pos[1];
const double* d = simplex->p_ + 3 * pos[2];
double ab[3], ac[3], ad[3];
ntcd__vec3_sub(ab, b, a);
ntcd__vec3_sub(ac, c, a);
ntcd__vec3_sub(ad, d, a);
////////////////////* Face Cases *///////////////////
/* On abc side */
double abxac[3];
ntcd__vec3_cross(abxac, ab, ac);
int abPerp1Pos, acPerp2Pos;
{
double cross_temp_a[3], cross_temp_b[3];
ntcd__vec3_cross(cross_temp_a, abxac, ab);
ntcd__vec3_cross(cross_temp_b, ac, abxac);
abPerp1Pos = (ntcd__vec3_dot(cross_temp_a, a) > 0.0);
acPerp2Pos = (ntcd__vec3_dot(cross_temp_b, a) > 0.0);
}
// The origin should be on abc's side and between the half-spaces defined by ac and ab (normal to abc)
{
double abcPerp[3];
if(ntcd__vec3_dot(abxac, ad) > 0.0) ntcd__vec3_smul(abcPerp, -1.0, abxac);
else memcpy(abcPerp, abxac, 3 * sizeof(*abcPerp));
if((ntcd__vec3_dot(abcPerp, a) < 0.0) && !abPerp1Pos && !acPerp2Pos){
/* Remove point d */
ntcd__simplex_remove_point(simplex, pos[2]);
memcpy(dir, abcPerp, 3 * sizeof(*dir));
break;
}
}
/* On abd side */
double abxad[3];
ntcd__vec3_cross(abxad, ab, ad);
int abPerp2Pos, adPerp1Pos;
{
double cross_temp_a[3], cross_temp_b[3];
ntcd__vec3_cross(cross_temp_a, abxad, ab);
ntcd__vec3_cross(cross_temp_b, ad, abxad);
abPerp2Pos = (ntcd__vec3_dot(cross_temp_a, a) > 0.0);
adPerp1Pos = (ntcd__vec3_dot(cross_temp_b, a) > 0.0);
}
// The origin should be on abd's side and between the half-spaces defined by ab and ad (normal to abd)
{
double abdPerp[3];
if(ntcd__vec3_dot(abxad, ac) > 0.0) ntcd__vec3_smul(abdPerp, -1.0, abxad);
else memcpy(abdPerp, abxad, 3 * sizeof(*abdPerp));
if((ntcd__vec3_dot(abdPerp, a) < 0.0) && !abPerp2Pos && !adPerp1Pos){
/* Remove point c */
ntcd__simplex_remove_point(simplex, pos[1]);
memcpy(dir, abdPerp, 3 * sizeof(*dir));
break;
}
}
/* On acd side */
double acxad[3];
ntcd__vec3_cross(acxad, ac, ad);
int acPerp1Pos, adPerp2Pos;
{
double cross_temp_a[3], cross_temp_b[3];
ntcd__vec3_cross(cross_temp_a, acxad, ac);
ntcd__vec3_cross(cross_temp_b, ad, acxad);
acPerp1Pos = (ntcd__vec3_dot(cross_temp_a, a) > 0.0);
adPerp2Pos = (ntcd__vec3_dot(cross_temp_b, a) > 0.0);
}
// The origin should be on acd's side and between the half-spaces defined by ac and ad (normal to acd)
{
double acdPerp[3];
if(ntcd__vec3_dot(acxad, ab) > 0.0) ntcd__vec3_smul(acdPerp, -1.0, acxad);
else memcpy(acdPerp, acxad, 3 * sizeof(*acdPerp));
if((ntcd__vec3_dot(acdPerp, a) < 0.0) && !acPerp1Pos && !adPerp2Pos){
/* Remove point b */
ntcd__simplex_remove_point(simplex, pos[0]);
memcpy(dir, acdPerp, 3 * sizeof(*dir));
break;
}
}
////////////////////* Edge Cases *///////////////////
/* ab Edge case */
// The origin must be inside the space defined by the intersection
// of two half-space normal to the adjacent faces abc, abd
if(abPerp1Pos && abPerp2Pos){
ntcd__vec3_triple_product(dir, a, ab, ab);
ntcd__simplex_remove_point(simplex, pos[1]);
ntcd__simplex_remove_point(simplex, pos[2]);
break;
}
/* ac Edge case */
// The origin must be inside the space defined by the intersection