convex.h

/*
Copyright (c) 2022 Ashley Rose Hale (LadyHavoc)

Permission is hereby granted, free of charge, to any person obtaining a copy
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The above copyright notice and this permission notice shall be included in
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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*/

// This module is a variant of the QuickHull algorithm intended to create hulls
// (brushes, aka n-sided polytopes or hulls) from a series of points provided by
// the caller

#pragma once

#ifndef CONVEX_H

enum convex_enums
{
	CONVEX_MAX_CORNERS = 256,
	CONVEX_MAX_FACES = 1024,
};

typedef struct convex_corner_s
{
	float x;
	float y;
	float z;
	float w; // 1.0f
}
convex_corner_t;

typedef struct convex_face_s
{
	// plane equation: a * x + b * y + c * z + d * w = 0.0f
	float x;
	float y;
	float z;
	float w;
}
convex_face_t;

typedef struct convex_builder_state_s
{
	// axially aligned bounding box
	float extents[2][3];

	int numcorners;
	convex_corner_t corners[CONVEX_MAX_CORNERS];

	int numfaces;
	convex_face_t faces[CONVEX_MAX_FACES];

	// we consider points to be equivalent if they are within this distance
	// suggested value is maxextent / 1048576.0f, which is a way of saying 
	// 'equivalent within 20 bits of precision'
	float epsilon;
}
convex_builder_state_t;

// set up a builer state to receive points
void convex_builder_initialize(convex_builder_state_t* b, float epsilon);

// this is a variant of QuickHull that relies on the caller to provide points
// in a reasonable order - the result will be the same regardless of point order
// but it's more efficient if the furthest points are provided first
//
// this could be a little more efficient if we kept track of edges during the
// build, but I think it may be more numerically stable this way
void convex_builder_add_point(convex_builder_state_t* b, float x, float y, float z);

// returns computed faces in array of vec4
// positivew=0 is for plane equations of the form a*x+b*y+c*z+w, which is the
// internal format
// positivew=1 is for plane equations of the form a*x+b*y+c*z-w, which tend to
// be less friendly in terms of vector ops
int convex_builder_get_planes4f(convex_builder_state_t* b, float* outplanes4f, int maxplanes, int positivew);

// returns the points as an array of vec3
// internal format is vec4, so this is just repacking the data
int convex_builder_get_points3f(convex_builder_state_t* b, float* outpoints3f, int maxpoints);

#endif