libs/math/frustum.h

/*
   Copyright (C) 2001-2006, William Joseph.
   All Rights Reserved.

   This file is part of GtkRadiant.

   GtkRadiant 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.

   GtkRadiant 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 GtkRadiant; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */

#if !defined( INCLUDED_MATH_FRUSTUM_H )
#define INCLUDED_MATH_FRUSTUM_H

/// \file
/// \brief View-frustum data types and related operations.

#include "generic/enumeration.h"
#include "math/matrix.h"
#include "math/plane.h"
#include "math/aabb.h"
#include "math/line.h"

inline Matrix4 matrix4_frustum( float left, float right, float bottom, float top, float nearval, float farval ){
	return Matrix4(
			   static_cast<float>( ( 2 * nearval ) / ( right - left ) ),
			   0,
			   0,
			   0,
			   0,
			   static_cast<float>( ( 2 * nearval ) / ( top - bottom ) ),
			   0,
			   0,
			   static_cast<float>( ( right + left ) / ( right - left ) ),
			   static_cast<float>( ( top + bottom ) / ( top - bottom ) ),
			   static_cast<float>( -( farval + nearval ) / ( farval - nearval ) ),
			   -1,
			   0,
			   0,
			   static_cast<float>( -( 2 * farval * nearval ) / ( farval - nearval ) ),
			   0
			   );
}


typedef unsigned char ClipResult;
const ClipResult c_CLIP_PASS = 0x00; // 000000
const ClipResult c_CLIP_LT_X = 0x01; // 000001
const ClipResult c_CLIP_GT_X = 0x02; // 000010
const ClipResult c_CLIP_LT_Y = 0x04; // 000100
const ClipResult c_CLIP_GT_Y = 0x08; // 001000
const ClipResult c_CLIP_LT_Z = 0x10; // 010000
const ClipResult c_CLIP_GT_Z = 0x20; // 100000
const ClipResult c_CLIP_FAIL = 0x3F; // 111111

template<typename Index>
class Vector4ClipLT
{
public:
static bool compare( const Vector4& self ){
	return self[Index::VALUE] < self[3];
}
static double scale( const Vector4& self, const Vector4& other ){
	return ( self[Index::VALUE] - self[3] ) / ( other[3] - other[Index::VALUE] );
}
};

template<typename Index>
class Vector4ClipGT
{
public:
static bool compare( const Vector4& self ){
	return self[Index::VALUE] > -self[3];
}
static double scale( const Vector4& self, const Vector4& other ){
	return ( self[Index::VALUE] + self[3] ) / ( -other[3] - other[Index::VALUE] );
}
};

template<typename ClipPlane>
class Vector4ClipPolygon
{
public:
typedef Vector4* iterator;
typedef const Vector4* const_iterator;

static std::size_t apply( const_iterator first, const_iterator last, iterator out ){
	const_iterator next = first, i = last - 1;
	iterator tmp( out );
	bool b0 = ClipPlane::compare( *i );
	while ( next != last )
	{
		bool b1 = ClipPlane::compare( *next );
		if ( b0 ^ b1 ) {
			*out = vector4_subtracted( *next, *i );

			double scale = ClipPlane::scale( *i, *out );

			( *out )[0] = static_cast<float>( ( *i )[0] + scale * ( ( *out )[0] ) );
			( *out )[1] = static_cast<float>( ( *i )[1] + scale * ( ( *out )[1] ) );
			( *out )[2] = static_cast<float>( ( *i )[2] + scale * ( ( *out )[2] ) );
			( *out )[3] = static_cast<float>( ( *i )[3] + scale * ( ( *out )[3] ) );

			++out;
		}

		if ( b1 ) {
			*out = *next;
			++out;
		}

		i = next;
		++next;
		b0 = b1;
	}

	return out - tmp;
}
};

#define CLIP_X_LT_W( p ) ( Vector4ClipLT< IntegralConstant<0> >::compare( p ) )
#define CLIP_X_GT_W( p ) ( Vector4ClipGT< IntegralConstant<0> >::compare( p ) )
#define CLIP_Y_LT_W( p ) ( Vector4ClipLT< IntegralConstant<1> >::compare( p ) )
#define CLIP_Y_GT_W( p ) ( Vector4ClipGT< IntegralConstant<1> >::compare( p ) )
#define CLIP_Z_LT_W( p ) ( Vector4ClipLT< IntegralConstant<2> >::compare( p ) )
#define CLIP_Z_GT_W( p ) ( Vector4ClipGT< IntegralConstant<2> >::compare( p ) )

inline ClipResult homogenous_clip_point( const Vector4& clipped ){
	ClipResult result = c_CLIP_FAIL;
	if ( CLIP_X_LT_W( clipped ) ) {
		result &= ~c_CLIP_LT_X;                    // X < W
	}
	if ( CLIP_X_GT_W( clipped ) ) {
		result &= ~c_CLIP_GT_X;                    // X > -W
	}
	if ( CLIP_Y_LT_W( clipped ) ) {
		result &= ~c_CLIP_LT_Y;                    // Y < W
	}
	if ( CLIP_Y_GT_W( clipped ) ) {
		result &= ~c_CLIP_GT_Y;                    // Y > -W
	}
	if ( CLIP_Z_LT_W( clipped ) ) {
		result &= ~c_CLIP_LT_Z;                    // Z < W
	}
	if ( CLIP_Z_GT_W( clipped ) ) {
		result &= ~c_CLIP_GT_Z;                    // Z > -W
	}
	return result;
}

/// \brief Clips \p point by canonical matrix \p self.
/// Stores the result in \p clipped.
/// Returns a bitmask indicating which clip-planes the point was outside.
inline ClipResult matrix4_clip_point( const Matrix4& self, const Vector3& point, Vector4& clipped ){
	clipped[0] = point[0];
	clipped[1] = point[1];
	clipped[2] = point[2];
	clipped[3] = 1;
	matrix4_transform_vector4( self, clipped );
	return homogenous_clip_point( clipped );
}


inline std::size_t homogenous_clip_triangle( Vector4 clipped[9] ){
	Vector4 buffer[9];
	std::size_t count = 3;
	count = Vector4ClipPolygon< Vector4ClipLT< IntegralConstant<0> > >::apply( clipped, clipped + count, buffer );
	count = Vector4ClipPolygon< Vector4ClipGT< IntegralConstant<0> > >::apply( buffer, buffer + count, clipped );
	count = Vector4ClipPolygon< Vector4ClipLT< IntegralConstant<1> > >::apply( clipped, clipped + count, buffer );
	count = Vector4ClipPolygon< Vector4ClipGT< IntegralConstant<1> > >::apply( buffer, buffer + count, clipped );
	count = Vector4ClipPolygon< Vector4ClipLT< IntegralConstant<2> > >::apply( clipped, clipped + count, buffer );
	return Vector4ClipPolygon< Vector4ClipGT< IntegralConstant<2> > >::apply( buffer, buffer + count, clipped );
}

/// \brief Transforms and clips the triangle formed by \p p0, \p p1, \p p2 by the canonical matrix \p self.
/// Stores the resulting polygon in \p clipped.
/// Returns the number of points in the resulting polygon.
inline std::size_t matrix4_clip_triangle( const Matrix4& self, const Vector3& p0, const Vector3& p1, const Vector3& p2, Vector4 clipped[9] ){
	clipped[0][0] = p0[0];
	clipped[0][1] = p0[1];
	clipped[0][2] = p0[2];
	clipped[0][3] = 1;
	clipped[1][0] = p1[0];
	clipped[1][1] = p1[1];
	clipped[1][2] = p1[2];
	clipped[1][3] = 1;
	clipped[2][0] = p2[0];
	clipped[2][1] = p2[1];
	clipped[2][2] = p2[2];
	clipped[2][3] = 1;

	matrix4_transform_vector4( self, clipped[0] );
	matrix4_transform_vector4( self, clipped[1] );
	matrix4_transform_vector4( self, clipped[2] );

	return homogenous_clip_triangle( clipped );
}

inline std::size_t homogenous_clip_line( Vector4 clipped[2] ){
	const Vector4& p0 = clipped[0];
	const Vector4& p1 = clipped[1];

	// early out
	{
		ClipResult mask0 = homogenous_clip_point( clipped[0] );
		ClipResult mask1 = homogenous_clip_point( clipped[1] );

		if ( ( mask0 | mask1 ) == c_CLIP_PASS ) { // both points passed all planes
			return 2;
		}

		if ( mask0 & mask1 ) { // both points failed any one plane
			return 0;
		}
	}

	{
		const bool index = CLIP_X_LT_W( p0 );
		if ( index ^ CLIP_X_LT_W( p1 ) ) {
			Vector4 clip( vector4_subtracted( p1, p0 ) );

			double scale = ( p0[0] - p0[3] ) / ( clip[3] - clip[0] );

			clip[0] = static_cast<float>( p0[0] + scale * clip[0] );
			clip[1] = static_cast<float>( p0[1] + scale * clip[1] );
			clip[2] = static_cast<float>( p0[2] + scale * clip[2] );
			clip[3] = static_cast<float>( p0[3] + scale * clip[3] );

			clipped[index] = clip;
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const bool index = CLIP_X_GT_W( p0 );
		if ( index ^ CLIP_X_GT_W( p1 ) ) {
			Vector4 clip( vector4_subtracted( p1, p0 ) );

			double scale = ( p0[0] + p0[3] ) / ( -clip[3] - clip[0] );

			clip[0] = static_cast<float>( p0[0] + scale * clip[0] );
			clip[1] = static_cast<float>( p0[1] + scale * clip[1] );
			clip[2] = static_cast<float>( p0[2] + scale * clip[2] );
			clip[3] = static_cast<float>( p0[3] + scale * clip[3] );

			clipped[index] = clip;
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const bool index = CLIP_Y_LT_W( p0 );
		if ( index ^ CLIP_Y_LT_W( p1 ) ) {
			Vector4 clip( vector4_subtracted( p1, p0 ) );

			double scale = ( p0[1] - p0[3] ) / ( clip[3] - clip[1] );

			clip[0] = static_cast<float>( p0[0] + scale * clip[0] );
			clip[1] = static_cast<float>( p0[1] + scale * clip[1] );
			clip[2] = static_cast<float>( p0[2] + scale * clip[2] );
			clip[3] = static_cast<float>( p0[3] + scale * clip[3] );

			clipped[index] = clip;
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const bool index = CLIP_Y_GT_W( p0 );
		if ( index ^ CLIP_Y_GT_W( p1 ) ) {
			Vector4 clip( vector4_subtracted( p1, p0 ) );

			double scale = ( p0[1] + p0[3] ) / ( -clip[3] - clip[1] );

			clip[0] = static_cast<float>( p0[0] + scale * clip[0] );
			clip[1] = static_cast<float>( p0[1] + scale * clip[1] );
			clip[2] = static_cast<float>( p0[2] + scale * clip[2] );
			clip[3] = static_cast<float>( p0[3] + scale * clip[3] );

			clipped[index] = clip;
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const bool index = CLIP_Z_LT_W( p0 );
		if ( index ^ CLIP_Z_LT_W( p1 ) ) {
			Vector4 clip( vector4_subtracted( p1, p0 ) );

			double scale = ( p0[2] - p0[3] ) / ( clip[3] - clip[2] );

			clip[0] = static_cast<float>( p0[0] + scale * clip[0] );
			clip[1] = static_cast<float>( p0[1] + scale * clip[1] );
			clip[2] = static_cast<float>( p0[2] + scale * clip[2] );
			clip[3] = static_cast<float>( p0[3] + scale * clip[3] );

			clipped[index] = clip;
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	{
		const bool index = CLIP_Z_GT_W( p0 );
		if ( index ^ CLIP_Z_GT_W( p1 ) ) {
			Vector4 clip( vector4_subtracted( p1, p0 ) );

			double scale = ( p0[2] + p0[3] ) / ( -clip[3] - clip[2] );

			clip[0] = static_cast<float>( p0[0] + scale * clip[0] );
			clip[1] = static_cast<float>( p0[1] + scale * clip[1] );
			clip[2] = static_cast<float>( p0[2] + scale * clip[2] );
			clip[3] = static_cast<float>( p0[3] + scale * clip[3] );

			clipped[index] = clip;
		}
		else if ( index == 0 ) {
			return 0;
		}
	}

	return 2;
}

/// \brief Transforms and clips the line formed by \p p0, \p p1 by the canonical matrix \p self.
/// Stores the resulting line in \p clipped.
/// Returns the number of points in the resulting line.
inline std::size_t matrix4_clip_line( const Matrix4& self, const Vector3& p0, const Vector3& p1, Vector4 clipped[2] ){
	clipped[0][0] = p0[0];
	clipped[0][1] = p0[1];
	clipped[0][2] = p0[2];
	clipped[0][3] = 1;
	clipped[1][0] = p1[0];
	clipped[1][1] = p1[1];
	clipped[1][2] = p1[2];
	clipped[1][3] = 1;

	matrix4_transform_vector4( self, clipped[0] );
	matrix4_transform_vector4( self, clipped[1] );

	return homogenous_clip_line( clipped );
}


struct Frustum
{
	Plane3 right, left, bottom, top, back, front;

	Frustum(){
	}
	Frustum( const Plane3& _right,
			 const Plane3& _left,
			 const Plane3& _bottom,
			 const Plane3& _top,
			 const Plane3& _back,
			 const Plane3& _front )
		: right( _right ), left( _left ), bottom( _bottom ), top( _top ), back( _back ), front( _front ){
	}
};

inline Frustum frustum_transformed( const Frustum& frustum, const Matrix4& transform ){
	return Frustum(
			   plane3_transformed( frustum.right, transform ),
			   plane3_transformed( frustum.left, transform ),
			   plane3_transformed( frustum.bottom, transform ),
			   plane3_transformed( frustum.top, transform ),
			   plane3_transformed( frustum.back, transform ),
			   plane3_transformed( frustum.front, transform )
			   );
}

inline Frustum frustum_inverse_transformed( const Frustum& frustum, const Matrix4& transform ){
	return Frustum(
			   plane3_inverse_transformed( frustum.right, transform ),
			   plane3_inverse_transformed( frustum.left, transform ),
			   plane3_inverse_transformed( frustum.bottom, transform ),
			   plane3_inverse_transformed( frustum.top, transform ),
			   plane3_inverse_transformed( frustum.back, transform ),
			   plane3_inverse_transformed( frustum.front, transform )
			   );
}

inline bool viewproj_test_point( const Matrix4& viewproj, const Vector3& point ){
	Vector4 hpoint( matrix4_transformed_vector4( viewproj, Vector4( point, 1.0f ) ) );
	if ( fabs( hpoint[0] ) < fabs( hpoint[3] )
		 && fabs( hpoint[1] ) < fabs( hpoint[3] )
		 && fabs( hpoint[2] ) < fabs( hpoint[3] ) ) {
		return true;
	}
	return false;
}

inline bool viewproj_test_transformed_point( const Matrix4& viewproj, const Vector3& point, const Matrix4& localToWorld ){
	return viewproj_test_point( viewproj, matrix4_transformed_point( localToWorld, point ) );
}

inline Frustum frustum_from_viewproj( const Matrix4& viewproj ){
	return Frustum
		   (
			   plane3_normalised( Plane3( viewproj[ 3] - viewproj[ 0], viewproj[ 7] - viewproj[ 4], viewproj[11] - viewproj[ 8], viewproj[15] - viewproj[12] ) ),
			   plane3_normalised( Plane3( viewproj[ 3] + viewproj[ 0], viewproj[ 7] + viewproj[ 4], viewproj[11] + viewproj[ 8], viewproj[15] + viewproj[12] ) ),
			   plane3_normalised( Plane3( viewproj[ 3] + viewproj[ 1], viewproj[ 7] + viewproj[ 5], viewproj[11] + viewproj[ 9], viewproj[15] + viewproj[13] ) ),
			   plane3_normalised( Plane3( viewproj[ 3] - viewproj[ 1], viewproj[ 7] - viewproj[ 5], viewproj[11] - viewproj[ 9], viewproj[15] - viewproj[13] ) ),
			   plane3_normalised( Plane3( viewproj[ 3] - viewproj[ 2], viewproj[ 7] - viewproj[ 6], viewproj[11] - viewproj[10], viewproj[15] - viewproj[14] ) ),
			   plane3_normalised( Plane3( viewproj[ 3] + viewproj[ 2], viewproj[ 7] + viewproj[ 6], viewproj[11] + viewproj[10], viewproj[15] + viewproj[14] ) )
		   );
}

struct VolumeIntersection
{
	enum Value
	{
		OUTSIDE,
		INSIDE,
		PARTIAL
	};
};

typedef EnumeratedValue<VolumeIntersection> VolumeIntersectionValue;

const VolumeIntersectionValue c_volumeOutside( VolumeIntersectionValue::OUTSIDE );
const VolumeIntersectionValue c_volumeInside( VolumeIntersectionValue::INSIDE );
const VolumeIntersectionValue c_volumePartial( VolumeIntersectionValue::PARTIAL );

inline VolumeIntersectionValue frustum_test_aabb( const Frustum& frustum, const AABB& aabb ){
	VolumeIntersectionValue result = c_volumeInside;

	switch ( aabb_classify_plane( aabb, frustum.right ) )
	{
	case 2:
		return c_volumeOutside;
	case 1:
		result = c_volumePartial;
	}

	switch ( aabb_classify_plane( aabb, frustum.left ) )
	{
	case 2:
		return c_volumeOutside;
	case 1:
		result = c_volumePartial;
	}

	switch ( aabb_classify_plane( aabb, frustum.bottom ) )
	{
	case 2:
		return c_volumeOutside;
	case 1:
		result = c_volumePartial;
	}

	switch ( aabb_classify_plane( aabb, frustum.top ) )
	{
	case 2:
		return c_volumeOutside;
	case 1:
		result = c_volumePartial;
	}

	switch ( aabb_classify_plane( aabb, frustum.back ) )
	{
	case 2:
		return c_volumeOutside;
	case 1:
		result = c_volumePartial;
	}

	switch ( aabb_classify_plane( aabb, frustum.front ) )
	{
	case 2:
		return c_volumeOutside;
	case 1:
		result = c_volumePartial;
	}

	return result;
}

inline double plane_distance_to_point( const Plane3& plane, const Vector3& point ){
	return vector3_dot( plane.normal(), point ) + plane.d;
}

inline double plane_distance_to_oriented_extents( const Plane3& plane, const Vector3& extents, const Matrix4& orientation ){
	return fabs( extents[0] * vector3_dot( plane.normal(), vector4_to_vector3( orientation.x() ) ) )
		   + fabs( extents[1] * vector3_dot( plane.normal(), vector4_to_vector3( orientation.y() ) ) )
		   + fabs( extents[2] * vector3_dot( plane.normal(), vector4_to_vector3( orientation.z() ) ) );
}

/// \brief Return false if \p aabb with \p orientation is partially or completely outside \p plane.
inline bool plane_contains_oriented_aabb( const Plane3& plane, const AABB& aabb, const Matrix4& orientation ){
	double dot = plane_distance_to_point( plane, aabb.origin );
	return !( dot > 0 || -dot < plane_distance_to_oriented_extents( plane, aabb.extents, orientation ) );
}

inline VolumeIntersectionValue frustum_intersects_transformed_aabb( const Frustum& frustum, const AABB& aabb, const Matrix4& localToWorld ){
	AABB aabb_world( aabb );
	matrix4_transform_point( localToWorld, aabb_world.origin );

	if ( plane_contains_oriented_aabb( frustum.right, aabb_world, localToWorld )
		 || plane_contains_oriented_aabb( frustum.left, aabb_world, localToWorld )
		 || plane_contains_oriented_aabb( frustum.bottom, aabb_world, localToWorld )
		 || plane_contains_oriented_aabb( frustum.top, aabb_world, localToWorld )
		 || plane_contains_oriented_aabb( frustum.back, aabb_world, localToWorld )
		 || plane_contains_oriented_aabb( frustum.front, aabb_world, localToWorld ) ) {
		return c_volumeOutside;
	}
	return c_volumeInside;
}

inline bool plane3_test_point( const Plane3& plane, const Vector3& point ){
	return vector3_dot( point, plane.normal() ) + plane.dist() <= 0;
}

inline bool plane3_test_line( const Plane3& plane, const Segment& segment ){
	return segment_classify_plane( segment, plane ) == 2;
}

inline bool frustum_test_point( const Frustum& frustum, const Vector3& point ){
	return !plane3_test_point( frustum.right, point )
		   && !plane3_test_point( frustum.left, point )
		   && !plane3_test_point( frustum.bottom, point )
		   && !plane3_test_point( frustum.top, point )
		   && !plane3_test_point( frustum.back, point )
		   && !plane3_test_point( frustum.front, point );
}

inline bool frustum_test_line( const Frustum& frustum, const Segment& segment ){
	return !plane3_test_line( frustum.right, segment )
		   && !plane3_test_line( frustum.left, segment )
		   && !plane3_test_line( frustum.bottom, segment )
		   && !plane3_test_line( frustum.top, segment )
		   && !plane3_test_line( frustum.back, segment )
		   && !plane3_test_line( frustum.front, segment );
}

inline bool viewer_test_plane( const Vector4& viewer, const Plane3& plane ){
	return ( ( plane.a * viewer[0] )
			 + ( plane.b * viewer[1] )
			 + ( plane.c * viewer[2] )
			 + ( plane.d * viewer[3] ) ) > 0;
}

inline Vector3 triangle_cross( const Vector3& p0, const Vector3& p1, const Vector3& p2 ){
	return vector3_cross( vector3_subtracted( p1, p0 ), vector3_subtracted( p1, p2 ) );
}

inline bool viewer_test_triangle( const Vector4& viewer, const Vector3& p0, const Vector3& p1, const Vector3& p2 ){
	Vector3 cross( triangle_cross( p0, p1, p2 ) );
	return ( ( viewer[0] * cross[0] )
			 + ( viewer[1] * cross[1] )
			 + ( viewer[2] * cross[2] )
			 + ( viewer[3] * 0 ) ) > 0;
}

inline Vector4 viewer_from_transformed_viewer( const Vector4& viewer, const Matrix4& transform ){
	if ( viewer[3] == 0 ) {
		return Vector4( matrix4_transformed_direction( transform, vector4_to_vector3( viewer ) ), 0 );
	}
	else
	{
		return Vector4( matrix4_transformed_point( transform, vector4_to_vector3( viewer ) ), viewer[3] );
	}
}

inline bool viewer_test_transformed_plane( const Vector4& viewer, const Plane3& plane, const Matrix4& localToWorld ){
#if 0
	return viewer_test_plane( viewer_from_transformed_viewer( viewer, matrix4_affine_inverse( localToWorld ) ), plane );
#else
	return viewer_test_plane( viewer, plane3_transformed( plane, localToWorld ) );
#endif
}

inline Vector4 viewer_from_viewproj( const Matrix4& viewproj ){
	// get viewer pos in object coords
	Vector4 viewer( matrix4_transformed_vector4( matrix4_full_inverse( viewproj ), Vector4( 0, 0, -1, 0 ) ) );
	if ( viewer[3] != 0 ) { // non-affine matrix
		viewer[0] /= viewer[3];
		viewer[1] /= viewer[3];
		viewer[2] /= viewer[3];
		viewer[3] /= viewer[3];
	}
	return viewer;
}

#endif