Geometric

The Geometric Functions defined in the OpenGL 4.6 Shading Language Specification.

#include <fennec/math/geometric.h> 

Geometric Functions

Syntax	Description
float dot(genFType x, genFType y) double dot(genDType x, genDType x)	Returns the dot product of \(x\) and \(y\), i.e., \(x_0 \cdot y_0 + x_1 \cdot y_1 + \ldots\). 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
float length2(genFType x) double length2(genDType x)	Returns the squared length of vector \(x\), i.e., \(x_0^2 + x_1^2 + \ldots\). 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
float length(genFType x) double length(genDType x)	Returns the length of vector \(x\), i.e., \(\sqrt{x_0^2 + x_1^2 + \ldots}\). 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
float distance(genFType x, genFType y) double distance(genDType x, genDType x)	Returns the length of vector \(x\), i.e., \(\sqrt{x_0^2 + x_1^2 + \ldots}\). 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
float normalize(genFType x) double normalize(genDType x)	Returns a vector in the same direction as \(x\), but with a length of \(1\), i.e. 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
vec3 cross(vec3 x, vec3 y) dvec3 cross(dvec3 x, dvec3 x)	Returns the cross product of \(x\) and \(y\), i.e., \(\left({x_1 \cdot y_2 - y_1 \cdot x_2, x_2 \cdot y_0 - y_2 \cdot x_0, x_0 \cdot y_1 - y_0 \cdot x_1}\right)\). 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
genFType faceforward(genFType N, genFType I, genFType Nref) genDType faceforward(genDType N, genDType I, genDType Nref)	If \(\text{dot}(Nref, I)<0\) return \(N\), otherwise return \(-N\). Returns \(N\) if \(\text{dot}(Nref,I)<0\), otherwise, returns \(-N\). Parameters N the vector I the incident Nref the reference
genFType reflect(genFType I, genFType N) genDType reflect(genDType I, genDType N)	For the incident vector \(I\) and surface orientation \(N\), returns the reflection direction. 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
genFType refract(genFType N, genFType I, float eta) genDType refract(genDType N, genDType I, double eta)	For the incident vector \(I\) and surface normal \(N\), and the ratio of indices of refraction \(eta\), return the refraction vector. 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