#include "GeomExport.h"
#include "point2.h"
#include "point3.h"
#include "geom_span.hpp"
#include <cstdint>

Classes
class	ITangentsComputationCallback
	This class is a callback for computing bump basis vectors on a given set of triangle/quad faces. More...

struct	UVTangentVectors
	Return value of ComputeUVTangents(). More...

Functions
Point3	BaryCoords (Point3 p0, Point3 p1, Point3 p2, Point3 p)
	Calculates the barycentric coordinates of the point p in 3-dimensional space according to a reference triangle indicated by its three vertices p0, p1 and p2.

Point3	BaryCoords (Point2 p0, Point2 p1, Point2 p2, Point2 p)
	Calculates the barycentric coordinates of the point p in 2-dimensional space according to a reference triangle indicated by its three vertices p0, p1 and p2.

bool	RayHitsBox (Ray &ray, Box3 &b)
	Checks if the given ray intersects a three-dimensional box.

float	DistPtToLine (Point2 p0, Point2 p1, Point2 *q)
	Calculates the distance of a given point from a line in two dimensions.

float	Dist3DPtToLine (Point3 p0, Point3 p1, Point3 *q)
	Calculates the distance of a given point from a line in three dimensions.

bool	ComputeIntersectionPoint (Point3 &intersectionPoint, geo::span< const Point3 > fixedCoeffs, geo::span< const Point3 > directionVecs, bool doNormalize=true)
	Compute the point of intersection, or a least squares approximation to it, for an arbitrary number N of lines in three dimensions.

void	ComputeBumpVectors (const Point3 tv[3], const Point3 v[3], Point3 bvec[3])

void	ComputeBumpVec2D (int axis, const Point3 tv[3], const Point3 v[3], Point3 bvec[2])
	Computes the 2 Bump basis vectors from the UV, VW, or WU at a triangle.

Point3	ComputeTangent (const Point3 tv[3], const Point3 v[3])
	returns the bump basis vector for the U texture channel (called the tangent)

void	ComputeTangentAndBinormal (const Point3 tv[3], const Point3 v[3], Point3 bvec[2])
	Computes the bump basis vector for the U texture channel (called the tangent), and the cross product of the surface normal with the tangent (called the binormal).

void	ComputeMikkTangents (ITangentsComputationCallback *tangentsComputationCallback)
	Computes the bump basis vector in MikkT way for the U texture channel (called the tangent), and the cross product of the surface normal with the tangent (called the binormal).

UVTangentVectors	ComputeUVTangents (const Point3 &p0, const Point3 &p1, const Point3 &p2, const Point2 &uv0, const Point2 &uv1, const Point2 &uv2)
	Computes the bump basis vectors for the U and V components of the texture coordinates channel (also called the tangent and bitangent).

uint32_t	CompressNormal (Point3 p)
	Low precision compression of a vector from 12 bytes to 4 bytes.

Point3	DeCompressNormal (uint32_t n)
	Decompresses a vector that was compressed using CompressNormal().

void	ArbAxis (const Point3 &zAxis, Matrix3 &matrix)
	Creates an arbitrary axis system given an up vector that conforms to the AutoCAD algorithm.

Function Documentation

◆ BaryCoords() [1/2]

Point3 BaryCoords	(	Point3	p0,
		Point3	p1,
		Point3	p2,
		Point3	p
	)

Calculates the barycentric coordinates of the point p in 3-dimensional space according to a reference triangle indicated by its three vertices p0, p1 and p2.

Parameters

p0,p1,p2	The three vertices of the reference triangle in 3-dimensional space.
p	The point for which the barycentric coordinates should be calculated.

Returns: Barycentric coordinates of point p.

See also: BaryCoords(Point2, Point2, Point2, Point2)

◆ BaryCoords() [2/2]

Point3 BaryCoords	(	Point2	p0,
		Point2	p1,
		Point2	p2,
		Point2	p
	)

Calculates the barycentric coordinates of the point p in 2-dimensional space according to a reference triangle indicated by its three vertices p0, p1 and p2.

Parameters

p0,p1,p2	The three vertices of the reference triangle in 2-dimensional space.
p	The point for which the barycentric coordinates should be calculated.

Returns: Barycentric coordinates of point p.

See also: BaryCoords(Point3, Point3, Point3, Point3)

◆ RayHitsBox()

bool RayHitsBox	(	Ray &	ray,
		Box3 &	b
	)

Checks if the given ray intersects a three-dimensional box.

Parameters

ray	The ray
b	The box

Returns: true if the ray intersects the box, false otherwise.

◆ DistPtToLine()

float DistPtToLine	(	Point2 *	p0,
		Point2 *	p1,
		Point2 *	q
	)

Calculates the distance of a given point from a line in two dimensions.

Parameters

p0,p1	Pointers to the two 2-dimensional points with which the line is defined.
q	Pointer to the 2-dimensional point whose distance from the line should be calculated.

Returns: The distance of the point from the line.

◆ Dist3DPtToLine()

float Dist3DPtToLine	(	Point3 *	p0,
		Point3 *	p1,
		Point3 *	q
	)

Calculates the distance of a given point from a line in three dimensions.

Parameters

p0,p1	Pointers to the two 3-dimensional points with which the line is defined.
q	Pointer to the 3-dimensional point whose distance from the line should be calculated.

Returns: The distance of the point from the line.

◆ ComputeIntersectionPoint()

bool ComputeIntersectionPoint	(	Point3 &	intersectionPoint,
		geo::span< const Point3 >	fixedCoeffs,
		geo::span< const Point3 >	directionVecs,
		bool	doNormalize = `true`
	)

Compute the point of intersection, or a least squares approximation to it, for an arbitrary number N of lines in three dimensions.

The ith of the N lines is presumed to be defined in terms of the parameter s_i according to:

x = fixedCoeffs[i] + s_i * (directionVecs[i])

A least squares problem is solved for the vector s' of parameters representing (the approximations to) the point of intersection, and intersectionPoint is computed by averaging estimates from each line, as:

intersectionPoint = (1 / N) * (SUM_OVER_I(fixedCoeffs[i] + s'_i * (directionVecs[i])))

Parameters

[out]	intersectionPoint	least squares approximation to intersection point
[in]	fixedCoeffs	fixed coefficients of line representation
[in]	directionVecs	line direction vectors
[in]	doNormalize	when true, normalized forms of the direction vectors are used in the least squares system

Returns: Flag indicating whether solution of least squares problem was successful. If it was not, intersectionPoint will be returned as a zero vector.

◆ ComputeBumpVectors()

void ComputeBumpVectors	(	const Point3	tv[3],
		const Point3	v[3],
		Point3	bvec[3]
	)

Deprecated:: Do not use this function. Use ComputeBumpVec2D() instead. This is here for compatibility only.

Computes the 3 bump basis vectors from the UVW coordinates of the triangle.

Parameters

	tv	Texture coordinates at 3 triangle vertices
	v	Coordinates of triangle vertices (usually in camera space).
[out]	bvec	The 3 bump basis vectors (normalized) corresponding to the U,V,and W axes.

◆ ComputeBumpVec2D()

void ComputeBumpVec2D	(	int	axis,
		const Point3	tv[3],
		const Point3	v[3],
		Point3	bvec[2]
	)

Computes the 2 Bump basis vectors from the UV, VW, or WU at a triangle.

Parameters

	axis	Either AXIS_UV, AXIS_VW, or AXIS_WU .
	tv	Texture coordinates at 3 triangle vertices.
	v	Coordinates of triangle vertices (usually in camera space)
[out]	bvec	The 2 normalized bump basis vectors corresponding to the specified axes.

Note: This is the recommended way to compute bump vectors instead of ComputeBumpVectors() which can give erroneous results.

◆ ComputeTangent()

Point3 ComputeTangent	(	const Point3	tv[3],
		const Point3	v[3]
	)

returns the bump basis vector for the U texture channel (called the tangent)

Parameters

tv	Texture coordinates at 3 triangle vertices.
v	Coordinates of triangle vertices (usually in camera space)

Returns: The 2 normalized bump basis vectors corresponding to the specified axes.

◆ ComputeTangentAndBinormal()

void ComputeTangentAndBinormal	(	const Point3	tv[3],
		const Point3	v[3],
		Point3	bvec[2]
	)

Computes the bump basis vector for the U texture channel (called the tangent), and the cross product of the surface normal with the tangent (called the binormal).

These along with the surface normal are used as the basis vectors for normal mapping.

Parameters

	tv	Texture coordinates at 3 triangle vertices.
	v	Coordinates of triangle vertices (usually in camera space)
[out]	bvec	The 2 normalized bump basis vectors corresponding to the specified axes.

◆ ComputeMikkTangents()

void ComputeMikkTangents ( ITangentsComputationCallback * tangentsComputationCallback )

Computes the bump basis vector in MikkT way for the U texture channel (called the tangent), and the cross product of the surface normal with the tangent (called the binormal).

These along with the surface normal are used as the basis vectors for normal mapping.

Parameters

tangentsComputationCallback The callback will be called during the computation to fill all required data and receive the results of computation.

◆ ComputeUVTangents()

UVTangentVectors ComputeUVTangents	(	const Point3 &	p0,
		const Point3 &	p1,
		const Point3 &	p2,
		const Point2 &	uv0,
		const Point2 &	uv1,
		const Point2 &	uv2
	)

Computes the bump basis vectors for the U and V components of the texture coordinates channel (also called the tangent and bitangent).

Remarks: This function differs from ComputeTangentAndBinormal() as the latter computes the binormal - the cross product of U tangent vector and normal - rather than the V tangent (or bitangent). The binormal and bitangent will differ if the U and V coordinates are not perpendicular to each other.

Parameters

p0	The XYZ coordinate of the first triangle vertex.
p1	The XYZ coordinate of the second triangle vertex.
p2	The XYZ coordinate of the third triangle vertex.
uv0	The UV coordinate of the first triangle vertex.
uv1	The UV coordinate of the second triangle vertex.
uv2	The UV coordinate of the third triangle vertex.

Returns: Two unit vectors in XYZ space, tangent to the surface of the given triangle, aligned with the U and V directions of the given texture coordinates.

◆ CompressNormal()

uint32_t CompressNormal ( Point3 p )

Low precision compression of a vector from 12 bytes to 4 bytes.

Only accurate to 1 part in 512. This is commonly used to compress normals. The vector has to be <= 1.0 in length.

Parameters

p	The decompressed vector.

Returns: The 4-byte long compressed value of p

See also: DeCompressNormal(), BMM_CHAN_NORMAL

◆ DeCompressNormal()

Point3 DeCompressNormal ( uint32_t n )

Decompresses a vector that was compressed using CompressNormal().

This function may also be used to decompress a surface normal from the G-Buffer using the BMM_CHAN_NORMAL channel. The decompressed vector has absolute error <.001 in each component.

Parameters

n	A vector compressed using CompressNormal()

Returns: A normalized decompressed normal vector

See also: CompressNormal()

◆ ArbAxis()

void ArbAxis	(	const Point3 &	zAxis,
		Matrix3 &	matrix
	)

Creates an arbitrary axis system given an up vector that conforms to the AutoCAD algorithm.

Parameters

	zAxis	The up vector.
[out]	matrix	The new axis system.

Classes

Functions

Function Documentation

◆ BaryCoords() [1/2]

◆ BaryCoords() [2/2]

◆ RayHitsBox()

◆ DistPtToLine()

◆ Dist3DPtToLine()

◆ ComputeIntersectionPoint()

◆ ComputeBumpVectors()

◆ ComputeBumpVec2D()

◆ ComputeTangent()

◆ ComputeTangentAndBinormal()

◆ ComputeMikkTangents()

◆ ComputeUVTangents()

◆ CompressNormal()

◆ DeCompressNormal()

◆ ArbAxis()