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/* Copyright (C) 1996-1997 Id Software, Inc.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
See file, 'COPYING', for details.
*/
#ifndef __COMMON_MATHLIB_H__
#define __COMMON_MATHLIB_H__
#include <float.h>
#include <math.h>
#include <common/cmdlib.hh>
#include <vector>
#include <set>
#include <array>
#include <utility>
#include <memory> // for unique_ptr
#include <glm/vec4.hpp>
#include <glm/vec3.hpp>
#include <glm/vec2.hpp>
#include <glm/glm.hpp>
#ifdef DOUBLEVEC_T
#define vec_t double
#define VECT_MAX DBL_MAX
#else
#define vec_t float
#define VECT_MAX FLT_MAX
#endif
typedef vec_t vec3_t[3];
typedef struct {
vec3_t normal;
vec_t dist;
} plane_t;
#define SIDE_FRONT 0
#define SIDE_ON 2
#define SIDE_BACK 1
#define SIDE_CROSS -2
#define Q_PI 3.14159265358979323846
#define DEG2RAD( a ) ( ( a ) * ( ( 2 * Q_PI ) / 360.0 ) )
extern const vec3_t vec3_origin;
#define EQUAL_EPSILON 0.001
#define ZERO_TRI_AREA_EPSILON 0.05f
#define POINT_EQUAL_EPSILON 0.05f
qboolean VectorCompare(const vec3_t v1, const vec3_t v2);
static inline bool
GLMVectorCompare(const glm::vec3 &v1, const glm::vec3 &v2)
{
for (int i = 0; i < 3; i++)
if (fabs(v1[i] - v2[i]) > EQUAL_EPSILON)
return false;
return true;
}
static inline vec_t
DotProduct(const vec3_t x, const vec3_t y)
{
return x[0] * y[0] + x[1] * y[1] + x[2] * y[2];
}
static inline void
VectorSubtract(const vec3_t x, const vec3_t y, vec3_t out)
{
out[0] = x[0] - y[0];
out[1] = x[1] - y[1];
out[2] = x[2] - y[2];
}
static inline void
VectorAdd(const vec3_t x, const vec3_t y, vec3_t out)
{
out[0] = x[0] + y[0];
out[1] = x[1] + y[1];
out[2] = x[2] + y[2];
}
static inline void
VectorCopy(const vec3_t in, vec3_t out)
{
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
static inline void
VectorScale(const vec3_t v, vec_t scale, vec3_t out)
{
out[0] = v[0] * scale;
out[1] = v[1] * scale;
out[2] = v[2] * scale;
}
static inline void
VectorInverse(vec3_t v)
{
v[0] = -v[0];
v[1] = -v[1];
v[2] = -v[2];
}
static inline void
VectorSet(vec3_t out, vec_t x, vec_t y, vec_t z)
{
out[0] = x;
out[1] = y;
out[2] = z;
}
static inline void
VectorCopyFromGLM(const glm::vec3 &in, vec3_t out)
{
out[0] = in.x;
out[1] = in.y;
out[2] = in.z;
}
static inline glm::vec3
VectorToGLM(const vec3_t in)
{
return glm::vec3(in[0], in[1], in[2]);
}
static inline vec_t
Q_rint(vec_t in)
{
return (vec_t)(floor(in + 0.5));
}
/*
Random()
returns a pseudorandom number between 0 and 1
*/
static inline vec_t
Random( void )
{
return (vec_t) rand() / RAND_MAX;
}
static inline void
VectorMA(const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc)
{
vc[0] = va[0] + scale * vb[0];
vc[1] = va[1] + scale * vb[1];
vc[2] = va[2] + scale * vb[2];
}
void CrossProduct(const vec3_t v1, const vec3_t v2, vec3_t cross);
static inline double
VectorLength(const vec3_t v)
{
int i;
double length;
length = 0;
for (i = 0; i < 3; i++)
length += v[i] * v[i];
length = sqrt(length);
return length;
}
static inline vec_t
VectorNormalize(vec3_t v)
{
int i;
double length;
length = 0;
for (i = 0; i < 3; i++)
length += v[i] * v[i];
length = sqrt(length);
if (length == 0)
return 0;
for (i = 0; i < 3; i++)
v[i] /= (vec_t)length;
return (vec_t)length;
}
// returns the normalized direction from `start` to `stop` in the `dir` param
// returns the distance from `start` to `stop`
static inline vec_t
GetDir(const vec3_t start, const vec3_t stop, vec3_t dir)
{
VectorSubtract(stop, start, dir);
return VectorNormalize(dir);
}
/* Shortcut for output of warnings/errors */
//FIXME: change from static buffers to returning std::string for thread safety
const char *VecStr(const vec3_t vec);
const char *VecStrf(const vec3_t vec);
// Maps uniform random variables U and V in [0, 1] to uniformly distributed points on a sphere
void UniformPointOnSphere(vec3_t dir, float u, float v);
void RandomDir(vec3_t dir);
glm::vec3 CosineWeightedHemisphereSample(float u1, float u2);
glm::mat3x3 RotateFromUpToSurfaceNormal(const glm::vec3 &surfaceNormal);
bool AABBsDisjoint(const vec3_t minsA, const vec3_t maxsA, const vec3_t minsB, const vec3_t maxsB);
void AABB_Init(vec3_t mins, vec3_t maxs, const vec3_t pt);
void AABB_Expand(vec3_t mins, vec3_t maxs, const vec3_t pt);
void AABB_Size(const vec3_t mins, const vec3_t maxs, vec3_t size_out);
void AABB_Grow(vec3_t mins, vec3_t maxs, const vec3_t size);
/**
* touching a side/edge/corner is considered touching
*/
template <int N, class T>
class qvec {
protected:
T v[N];
public:
qvec() {
for (int i=0; i<N; i++)
v[i] = 0;
}
qvec(const T &a) {
for (int i=0; i<N; i++)
v[i] = a;
}
qvec(const T &a, const T &b) {
v[0] = a;
v[1] = b;
for (int i=2; i<N; i++)
v[i] = 0;
}
qvec(const T &a, const T &b, const T &c) {
v[0] = a;
v[1] = b;
v[2] = c;
for (int i=3; i<N; i++)
v[i] = 0;
}
qvec(const T &a, const T &b, const T &c, const T &d) {
v[0] = a;
v[1] = b;
v[2] = c;
v[3] = d;
for (int i=4; i<N; i++)
v[i] = 0;
}
bool operator==(const qvec<N,T> &other) const {
for (int i=0; i<N; i++)
if (v[i] != other.v[i])
return false;
return true;
}
T operator[](const size_t idx) const {
return v[idx];
}
T &operator[](const size_t idx) {
return v[idx];
}
void operator+=(const qvec<N,T> &other) {
for (int i=0; i<N; i++)
v[i] += other.v[i];
}
void operator-=(const qvec<N,T> &other) {
for (int i=0; i<N; i++)
v[i] -= other.v[i];
}
void operator*=(const T &scale) {
for (int i=0; i<N; i++)
v[i] *= scale;
}
void operator/=(const T &scale) {
for (int i=0; i<N; i++)
v[i] /= scale;
}
qvec<N,T> operator+(const qvec<N,T> &other) const {
qvec<N,T> res(*this);
res += other;
return res;
}
qvec<N,T> operator-(const qvec<N,T> &other) const {
qvec<N,T> res(*this);
res -= other;
return res;
}
qvec<N,T> operator*(const T &scale) const {
qvec<N,T> res(*this);
res *= scale;
return res;
}
qvec<N,T> operator/(const T &scale) const {
qvec<N,T> res(*this);
res /= scale;
return res;
}
};
using qvec2f = qvec<2, float>;
using qvec3f = qvec<3, float>;
/**
* touching a side/edge/corner is considered touching
*/
template <int N, class V>
class aabb {
private:
V m_mins, m_maxs;
void fix() {
for (int i=0; i<N; i++) {
if (m_maxs[i] < m_mins[i]) {
m_maxs[i] = m_mins[i];
}
}
}
public:
aabb(const V &mins, const V &maxs) : m_mins(mins), m_maxs(maxs) {
fix();
}
aabb(const aabb<N,V> &other) : m_mins(other.m_mins), m_maxs(other.m_maxs) {
fix();
}
bool operator==(const aabb<N,V> &other) const {
return m_mins == other.m_mins
&& m_maxs == other.m_maxs;
}
const V &mins() const {
return m_mins;
}
const V &maxs() const {
return m_maxs;
}
bool disjoint(const aabb<N,V> &other) const {
for (int i=0; i<N; i++) {
if (m_maxs[i] < other.m_mins[i]) return true;
if (m_mins[i] > other.m_maxs[i]) return true;
}
return false;
}
bool contains(const aabb<N,V> &other) const {
for (int i=0; i<3; i++) {
if (other.m_mins[i] < m_mins[i])
return false;
if (other.m_maxs[i] > m_maxs[i])
return false;
}
return true;
}
bool containsPoint(const V &p) const {
for (int i=0; i<N; i++) {
if (!(p[i] >= m_mins[i] && p[i] <= m_maxs[i])) return false;
}
return true;
}
aabb<N,V> expand(const V &pt) const {
V mins, maxs;
for (int i=0; i<N; i++) {
mins[i] = qmin(m_mins[i], pt[i]);
maxs[i] = qmax(m_maxs[i], pt[i]);
}
return aabb<N,V>(mins, maxs);
}
aabb<N,V> unionWith(const aabb<N,V> &other) const {
return expand(other.m_mins).expand(other.m_maxs);
}
std::pair<bool, aabb<N,V>> intersectWith(const aabb<N,V> &other) const {
V mins, maxs;
for (int i=0; i<N; i++) {
mins[i] = qmax(m_mins[i], other.m_mins[i]);
maxs[i] = qmin(m_maxs[i], other.m_maxs[i]);
if (mins[i] > maxs[i]) {
// empty intersection
return std::make_pair(false, aabb<N,V>(qvec3f(0), qvec3f(0)));
}
}
return std::make_pair(true, aabb<N,V>(mins, maxs));
}
V size() const {
V result = m_maxs - m_mins;
return result;
}
aabb<N,V> grow(const V &size) const {
return aabb<N,V>(m_mins - size, m_maxs + size);
}
};
using aabb3 = aabb<3, qvec3f>;
using aabb2 = aabb<2, qvec2f>;
using tri_t = std::tuple<glm::vec3, glm::vec3, glm::vec3>;
/// abc - clockwise ordered triangle
/// p - point to get the barycentric coords of
glm::vec3 Barycentric_FromPoint(const glm::vec3 &p, const tri_t &tri);
glm::vec3 Barycentric_Random(const float r1, const float r2);
/// Evaluates the given barycentric coord for the given triangle
glm::vec3 Barycentric_ToPoint(const glm::vec3 &bary,
const tri_t &tri);
vec_t TriangleArea(const vec3_t v0, const vec3_t v1, const vec3_t v2);
// noramlizes the given pdf so it sums to 1, then converts to a cdf
std::vector<float> MakeCDF(const std::vector<float> &pdf);
int SampleCDF(const std::vector<float> &cdf, float sample);
// filtering
// width (height) are the filter "radius" (not "diameter")
float Filter_Gaussian(float width, float height, float x, float y);
// sqrt(x^2 + y^2) should be <= a, returns 0 outside that range.
float Lanczos2D(float x, float y, float a);
// glm geometry
static inline glm::vec3 vec3_t_to_glm(const vec3_t vec) {
return glm::vec3(vec[0], vec[1], vec[2]);
}
static inline void glm_to_vec3_t(const glm::vec3 &glm, vec3_t out) {
out[0] = glm.x;
out[1] = glm.y;
out[2] = glm.z;
}
// Returns (0 0 0) if we couldn't determine the normal
glm::vec3 GLM_FaceNormal(std::vector<glm::vec3> points);
std::pair<bool, glm::vec4> GLM_MakeInwardFacingEdgePlane(const glm::vec3 &v0, const glm::vec3 &v1, const glm::vec3 &faceNormal);
std::vector<glm::vec4> GLM_MakeInwardFacingEdgePlanes(const std::vector<glm::vec3> &points);
bool GLM_EdgePlanes_PointInside(const std::vector<glm::vec4> &edgeplanes, const glm::vec3 &point);
float GLM_EdgePlanes_PointInsideDist(const std::vector<glm::vec4> &edgeplanes, const glm::vec3 &point);
glm::vec3 GLM_TriangleCentroid(const glm::vec3 &v0, const glm::vec3 &v1, const glm::vec3 &v2);
float GLM_TriangleArea(const glm::vec3 &v0, const glm::vec3 &v1, const glm::vec3 &v2);
float GLM_DistAbovePlane(const glm::vec4 &plane, const glm::vec3 &point);
glm::vec3 GLM_ProjectPointOntoPlane(const glm::vec4 &plane, const glm::vec3 &point);
float GLM_PolyArea(const std::vector<glm::vec3> &points);
glm::vec3 GLM_PolyCentroid(const std::vector<glm::vec3> &points);
glm::vec4 GLM_PolyPlane(const std::vector<glm::vec3> &points);
/// Returns the index of the polygon edge, and the closest point on that edge, to the given point
std::pair<int, glm::vec3> GLM_ClosestPointOnPolyBoundary(const std::vector<glm::vec3> &poly, const glm::vec3 &point);
/// Returns `true` and the interpolated normal if `point` is in the polygon, otherwise returns false.
std::pair<bool, glm::vec3> GLM_InterpolateNormal(const std::vector<glm::vec3> &points,
const std::vector<glm::vec3> &normals,
const glm::vec3 &point);
std::vector<glm::vec3> GLM_ShrinkPoly(const std::vector<glm::vec3> &poly, const float amount);
/// Returns (front part, back part)
std::pair<std::vector<glm::vec3>,std::vector<glm::vec3>> GLM_ClipPoly(const std::vector<glm::vec3> &poly, const glm::vec4 &plane);
glm::vec3 GLM_PolyRandomPoint(const std::vector<glm::vec3> &points);
/// projects p onto the vw line.
/// returns 0 for p==v, 1 for p==w
float FractionOfLine(const glm::vec3 &v, const glm::vec3 &w, const glm::vec3& p);
// Returns weights for f(0,0), f(1,0), f(0,1), f(1,1)
// from: https://en.wikipedia.org/wiki/Bilinear_interpolation#Unit_Square
static inline glm::vec4 bilinearWeights(const float x, const float y) {
Q_assert(x >= 0.0f);
Q_assert(x <= 1.0f);
Q_assert(y >= 0.0f);
Q_assert(y <= 1.0f);
return glm::vec4((1.0f - x) * (1.0f - y), x * (1.0f - y), (1.0f - x) * y, x * y);
}
// This uses a coordinate system where the pixel centers are on integer coords.
// e.g. the corners of a 3x3 pixel bitmap are at (-0.5, -0.5) and (2.5, 2.5).
static inline std::array<std::pair<glm::ivec2, float>, 4>
bilinearWeightsAndCoords(glm::vec2 pos, const glm::ivec2 &size)
{
Q_assert(pos.x >= -0.5f && pos.x <= (size.x - 0.5f));
Q_assert(pos.y >= -0.5f && pos.y <= (size.y - 0.5f));
// Handle extrapolation.
for (int i=0; i<2; i++) {
if (pos[i] < 0)
pos[i] = 0;
if (pos[i] > (size[i] - 1))
pos[i] = (size[i] - 1);
}
Q_assert(pos.x >= 0.f && pos.x <= (size.x - 1));
Q_assert(pos.y >= 0.f && pos.y <= (size.y - 1));
glm::ivec2 integerPart(glm::floor(pos));
glm::vec2 fractionalPart(pos - glm::floor(pos));
// ensure integerPart + (1, 1) is still in bounds
for (int i=0; i<2; i++) {
if (fractionalPart[i] == 0.0f && integerPart[i] > 0) {
integerPart[i] -= 1;
fractionalPart[i] = 1.0f;
}
}
Q_assert(integerPart.x + 1 < size.x);
Q_assert(integerPart.y + 1 < size.y);
Q_assert(glm::vec2(integerPart) + fractionalPart == pos);
// f(0,0), f(1,0), f(0,1), f(1,1)
const glm::vec4 weights = bilinearWeights(fractionalPart.x, fractionalPart.y);
std::array<std::pair<glm::ivec2, float>, 4> result;
for (int i=0; i<4; i++) {
const float weight = weights[i];
glm::ivec2 pos(integerPart);
if ((i % 2) == 1)
pos.x += 1;
if (i >= 2)
pos.y += 1;
Q_assert(pos.x >= 0);
Q_assert(pos.x < size.x);
Q_assert(pos.y >= 0);
Q_assert(pos.y < size.y);
result[i] = std::make_pair(pos, weight);
}
return result;
}
template <typename V>
V bilinearInterpolate(const V &f00, const V &f10, const V &f01, const V &f11, const float x, const float y)
{
glm::vec4 weights = bilinearWeights(x,y);
const V fxy = f00 * weights[0] + \
f10 * weights[1] + \
f01 * weights[2] + \
f11 * weights[3];
return fxy;
}
template <typename V>
std::vector<V> PointsAlongLine(const V &start, const V &end, const float step)
{
const V linesegment = end - start;
const float len = glm::length(linesegment);
if (len == 0)
return {};
std::vector<V> result;
const V dir = linesegment / len;
const int stepCount = static_cast<int>(len / step);
for (int i=0; i<=stepCount; i++) {
const V pt = start + (dir * (step * i));
result.push_back(pt);
}
return result;
}
// octree
aabb3 bboxOctant(const aabb3 &box, int i);
#define MAX_OCTREE_DEPTH 3
using octree_nodeid = int;
template <typename T>
class octree_node_t {
public:
int m_depth;
aabb3 m_bbox;
bool m_leafNode;
std::vector<std::pair<aabb3, T>> m_leafObjects; // only nonempty if m_leafNode
octree_nodeid m_children[8]; // only use if !m_leafNode
octree_node_t(const aabb3 &box, const int depth) :
m_depth(depth),
m_bbox(box),
m_leafNode(true),
m_leafObjects()
{
Q_assert(m_depth <= MAX_OCTREE_DEPTH);
}
};
template <typename T>
class octree_t {
private:
std::vector<octree_node_t<T>> m_nodes;
/**
* helper for toNode().
*
* creates the ith octant child of `thisNode`, and adds it to the end of `octree`.
* returns the nodeid.
*/
octree_nodeid createChild(octree_nodeid thisNode, int i) {
octree_node_t<T> *node = &m_nodes[thisNode];
const aabb3 childBox = bboxOctant(node->m_bbox, i);
octree_node_t<T> newNode(childBox, node->m_depth + 1);
m_nodes.push_back(newNode); // invalidates `node` reference
return static_cast<int>(m_nodes.size() - 1);
}
void toNode(octree_nodeid thisNode) {
octree_nodeid newNodeIds[8];
for (int i=0; i<8; i++) {
newNodeIds[i] = createChild(thisNode, i);
}
octree_node_t<T> *node = &m_nodes[thisNode];
Q_assert(node->m_leafNode);
Q_assert(node->m_leafObjects.empty()); // we always convert leafs to nodes before adding anything
for (int i=0; i<8; i++) {
node->m_children[i] = newNodeIds[i];
}
node->m_leafNode = false;
}
void queryTouchingBBox(octree_nodeid thisNode, const aabb3 &query, std::set<T> &dest) const {
const octree_node_t<T> *node = &m_nodes[thisNode];
if (node->m_leafNode) {
// Test all objects
for (const auto &boxObjPair : node->m_leafObjects) {
if (!query.disjoint(boxObjPair.first)) {
dest.insert(boxObjPair.second);
}
}
return;
}
// Test all children that intersect the query
for (int i=0; i<8; i++) {
const octree_nodeid child_i_index = node->m_children[i];
const octree_node_t<T> *child_i_node = &m_nodes[child_i_index];
const std::pair<bool, aabb3> intersection = query.intersectWith(child_i_node->m_bbox);
if (intersection.first) {
queryTouchingBBox(child_i_index, intersection.second, dest);
}
}
}
void insert(octree_nodeid thisNode, const aabb3 &objBox, const T &obj) {
octree_node_t<T> *node = &m_nodes[thisNode];
Q_assert(node->m_bbox.contains(objBox));
if (node->m_leafNode && node->m_depth < MAX_OCTREE_DEPTH) {
toNode(thisNode);
// N.B.: `node` pointer was invalidated
node = &m_nodes[thisNode];
}
if (node->m_leafNode) {
node->m_leafObjects.push_back(std::make_pair(objBox, obj));
return;
}
// inserting into a non-leaf node
for (int i=0; i<8; i++) {
const octree_nodeid child_i_index = node->m_children[i];
octree_node_t<T> *child_i_node = &m_nodes[child_i_index];
const std::pair<bool, aabb3> intersection = objBox.intersectWith(child_i_node->m_bbox);
if (intersection.first) {
insert(child_i_index, intersection.second, obj);
// N.B.: `node` pointer was invalidated
node = &m_nodes[thisNode];
}
}
}
public:
void insert(const aabb3 &objBox, const T &obj) {
insert(0, objBox, obj);
}
std::vector<T> queryTouchingBBox(const aabb3 &query) const {
std::set<T> res;
queryTouchingBBox(0, query, res);
std::vector<T> res_vec;
for (const auto &item : res) {
res_vec.push_back(item);
}
return res_vec;
}
octree_t(const aabb3 &box) {
this->m_nodes.push_back(octree_node_t<T>(box, 0));
}
};
template <typename T>
octree_t<T> makeOctree(const std::vector<std::pair<aabb3, T>> &objects)
{
if (objects.empty()) {
octree_t<T> empty{aabb3{qvec3f(), qvec3f()}};
return empty;
}
// take bbox of objects
aabb3 box = objects.at(0).first;
for (const auto &pr : objects) {
box = box.unionWith(pr.first);
}
octree_t<T> res(box);
for (const auto &pr : objects) {
res.insert(pr.first, pr.second);
}
return res;
}
// mesh_t
class mesh_t {
public:
std::vector<glm::vec3> verts;
std::vector<std::vector<int>> faces;
};
// Welds vertices at exactly the same position
mesh_t buildMesh(const std::vector<std::vector<glm::vec3>> &faces);
std::vector<std::vector<glm::vec3>> meshToFaces(const mesh_t &mesh);
// Preserves the number and order of faces.
// doesn't merge verts.
// adds verts to fix t-juncs
void cleanupMesh(mesh_t &mesh);
#endif /* __COMMON_MATHLIB_H__ */
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