#include <fennec/math/vector.h>
#include <fennec/math/common.h>
#include <fennec/math/exponential.h>

Detailed Description

Author: Medusa Slockbower

Copyright: Copyright © 2025 Medusa Slockbower (GPLv3)

Functions
template<typename genType , size_t... i>
constexpr genType	fennec::dot (const vector< genType, i... > &x, const vector< genType, i... > &y)
	Returns the dot product of \(x\) and \(y\), i.e., \(x_0 \cdot y_0 + x_1 \cdot y_1 + \ldots\).

template<typename genType , size_t... i>
constexpr genType	fennec::length2 (const vector< genType, i... > &x)
	Returns the squared length of vector \(x\), i.e., \(x_0^2 + x_1^2 + \ldots\).

template<typename genType , size_t... i>
constexpr genType	fennec::length (const vector< genType, i... > &x)
	Returns the length of vector \(x\), i.e., \(\sqrt{x_0^2 + x_1^2 + \ldots}\).

template<typename genType , size_t... i>
constexpr genType	fennec::distance (const vector< genType, i... > &p0, const vector< genType, i... > &p1)
	Returns the length of vector \(x\), i.e., \(\sqrt{x_0^2 + x_1^2 + \ldots}\).

template<typename genType , size_t... i> requires (sizeof...(i) == 3)
constexpr vector< genType, i... >	fennec::cross (const vector< genType, i... > &x, const vector< genType, i... > &y)
	Returns the cross product of \(x\) and \(y\), i.e., \(\left({x_1 \cdot y_2 - y_1 \cdot x_2, x_2 \cdot y_0 - y_2 \cdot x_0, x_0 \cdot y_1 - y_0 \cdot x_1}\right)\).

template<typename genType , size_t... i>
constexpr vector< genType, i... >	fennec::normalize (const vector< genType, i... > &x)
	Returns a vector in the same direction as \(x\), but with a length of \(1\), i.e.

template<typename genType , size_t... i>
constexpr vector< genType, i... >	fennec::faceforward (const vector< genType, i... > &N, const vector< genType, i... > &I, const vector< genType, i... > &Nref)
	If \(\text{dot}(Nref, I)<0\) return \(N\), otherwise return \(-N\).

template<typename genType , size_t... i>
constexpr vector< genType, i... >	fennec::reflect (const vector< genType, i... > &I, const vector< genType, i... > &N)
	For the incident vector \(I\) and surface orientation \(N\), returns the reflection direction.

template<typename genType , size_t... i>
constexpr vector< genType, i... >	fennec::refract (const vector< genType, i... > &I, const vector< genType, i... > &N, genType eta)
	For the incident vector \(I\) and surface normal \(N\), and the ratio of indices of refraction \(eta\), return the refraction vector.

Function Documentation

◆ dot()

template<typename genType , size_t... i>

constexpr genType fennec::dot	(	const vector< genType, i... > &	x,
		const vector< genType, i... > &	y
	)

constexpr

Returns: the dot product of \(x\) and \(y\), i.e., \(x_0 \cdot y_0 + x_0 \cdot y_0 + \ldots\)

we can represent this in linear algebra as the following,

let \(X=\left[\begin{array}\\ x_0 \\ x_1 \\ \vdots \\ x_N \end{array}\right]\)
let \(Y=\left[\begin{array}\\ y_0 \\ y_1 \\ \vdots \\ y_N \end{array}\right]\)

then \(\text{dot}(X, Y)=X \cdot Y^T\)

Parameters

x	first vector
y	second vector

◆ length2()

template<typename genType , size_t... i>

constexpr genType fennec::length2 ( const vector< genType, i... > & x )

constexpr

Returns: the squared length of vector \(x\), i.e., \(x_0^2 + x_1^2 + \ldots\)

we can represent this in linear algebra as the following,

let \(X=\left[\begin{array}\\ x_0 \\ x_1 \\ \vdots \\ x_N \end{array}\right]\)

then \(\text{length2}(X)=X \cdot X^T\)

Parameters

x	the vector

◆ length()

template<typename genType , size_t... i>

constexpr genType fennec::length ( const vector< genType, i... > & x )

constexpr

Returns: the length of vector \(x\), i.e., \(\sqrt{x_0^2 + x_1^2 + \ldots}\)

we can represent this in linear algebra as the following,

let \(X=\left[\begin{array}\\ x_0 \\ x_1 \\ \vdots \\ x_N \end{array}\right]\)

then, \(\text{length}(X)=\left|\left|X\right|\right|\)

Parameters

x	the vector

◆ distance()

template<typename genType , size_t... i>

constexpr genType fennec::distance	(	const vector< genType, i... > &	p0,
		const vector< genType, i... > &	p1
	)

constexpr

Returns: the distance between \(p_0\) and \(p_1\), i.e., \(\left|{p_1-p_0}\right|\)

we can represent this in linear algebra as the following,

let \(X=\left[\begin{array}\\ x_0 \\ x_1 \\ \vdots \\ x_N \end{array}\right]\)
let \(Y=\left[\begin{array}\\ y_0 \\ y_1 \\ \vdots \\ y_N \end{array}\right]\)

then \(\text{distance}(X, Y)=\left|\left|Y-X\right|\right|\)

Parameters

p0	first vector
p1	second vector

◆ cross()

template<typename genType , size_t... i>
requires (sizeof...(i) == 3)

constexpr vector< genType, i... > fennec::cross	(	const vector< genType, i... > &	x,
		const vector< genType, i... > &	y
	)

constexpr

Returns: the cross product of \(x\) and \(y\), i.e., \(\left({x_1 \cdot y_2 - y_1 \cdot x_2, x_2 \cdot y_0 - y_2 \cdot x_0, x_0 \cdot y_1 - y_0 \cdot x_1}\right)\)

we can represent this in linear algebra as the following,

let \(X=\left[\begin{array}\\ x_0 \\ x_1 \\ \vdots \\ x_N \end{array}\right]\)
let \(Y=\left[\begin{array}\\ y_0 \\ y_1 \\ \vdots \\ y_N \end{array}\right]\)

then \(\text{cross}(X, Y)=X \times Y\)

Parameters

x	first vector
y	second vector

◆ normalize()

template<typename genType , size_t... i>

constexpr vector< genType, i... > fennec::normalize ( const vector< genType, i... > & x )

constexpr

Returns: a vector in the same direction as \(x\), but with a length of \(1\), i.e. \(\frac{x}{||x||}\)

we can represent this in linear algebra as the following,

let \(X=\left[\begin{array}\\ x_0 \\ x_1 \\ \vdots \\ x_N \end{array}\right]\)

then, \(\text{length}(X)=\frac{X}{\left|\left|X\right|\right|}\)

Parameters

x

◆ faceforward()

template<typename genType , size_t... i>

constexpr vector< genType, i... > fennec::faceforward	(	const vector< genType, i... > &	N,
		const vector< genType, i... > &	I,
		const vector< genType, i... > &	Nref
	)

constexpr

Returns: \(N\) if \(\text{dot}(Nref,I)<0\), otherwise, returns \(-N\).

Parameters

N	the vector
I	the incident
Nref	the reference

◆ reflect()

template<typename genType , size_t... i>

constexpr vector< genType, i... > fennec::reflect	(	const vector< genType, i... > &	I,
		const vector< genType, i... > &	N
	)

constexpr

Returns: The reflection direction, given the incident vector \(I\) and surface orientation \(N\)

We can express this as,

\(\text{reflect}(I, N) = I - 2 N \cdot \text{dot}(N, I)\)

Parameters

I	the incident
N	the surface orientation

◆ refract()

template<typename genType , size_t... i>

constexpr vector< genType, i... > fennec::refract	(	const vector< genType, i... > &	I,
		const vector< genType, i... > &	N,
		genType	eta
	)

constexpr

Returns: The refraction vector, given the incident vector \(I\), surface normal \(N\), and ratio \(eta\).

The result is computed by the refraction equation,

let \(k=1.0-eta^2 \cdot (1.0 - \text{dot}(N, I)^2)\)
then, \(\text{refract}(I, N, eta)=\begin{cases} 0.0 & k<0.0, \\ eta \cdot I - N \cdot (eta \cdot \text{dot}(N, I) + \sqrt{k}) \end{cases}\)

Parameters

I	the incident
N	the surface normal
eta	the ratio of indices of refraction

Detailed Description

Functions

Function Documentation

◆ dot()

◆ length2()

◆ length()

◆ distance()

◆ cross()

◆ normalize()

◆ faceforward()

◆ reflect()

◆ refract()