Geometry Functions

NoticeThe functions listed below are the members of the Unigine.MathLib namespace.

This class is used to represent a collection of generic 3d math functions such as line plane intersection, closest points on two lines, etc.

Methods:

Name	Description View: Sort by:
OrthoBasis	Creates an ortho transformation.
OrthoTransform	Creates an ortho transformation.
OrthoTangent	Creates the ortho triangle tangent space basis.
TriangleArea	Returns the triangle area.
TriangleNormal	Returns the triangle normal vector.
TrianglePlane	Returns the triangle plane.
TriangleTangent	Returns the triangle tangent space.
PolygonPlane	Returns the polygon plane.
PointTriangleInside	Checks if a point is inside a triangle.
PointTriangleDistance	Returns the closest distance from a point to a triangle.
PointTriangleCoordinates	Calculates barycentric triangle coordinates.
PointPolygonDistance	Returns the distance from a point to a polygon.
RayBoundBoxIntersection	Checks if a ray intersects a bounding box.
IRayBoundBoxIntersection	Checks if there is an intersection between a ray and a bounding box.
RayTriangleIntersection	Checks if a ray intersects a triangle.
LinePlaneIntersection	Checks if there is an intersection between a line and a plane.
RayPlaneIntersection	Checks if there is an intersection between a ray and a plane.
SegmentPlaneIntersection	Checks if a segment intersects a plane.
GetClosestPointOnLine	Scans the specified line segment and returns the point closest to the reference point.
GetClosestPointOnTriangle	Scans the specified triangle and searches for the point closest to the reference point.
GetClosestPointsOnLines	Scans the two specified lines and searches for the pair of closest points.
ProjectOntoPlane	Calculates the projection of a vector onto a given plane.
TriangleRasterize	Positions the given triangle within the given screen coordinates, rasterizes it and applies the specified shader to each pixel.

Geometry Class

Members

void OrthoBasis ( vec3 v, vec3 tangent, vec3 binormal ) #

Creates an ortho transformation. Output tangent and binormal vectors will be put to corresponding return vectors.

Arguments

vec3 v - Input vector.
vec3 tangent - Return tangent vector.
vec3 binormal - Return binormal vector.

void OrthoBasis ( dvec3 v, dvec3 tangent, dvec3 binormal ) #

Creates an ortho transformation. Output tangent and binormal vectors will be put to corresponding return vectors.

Arguments

dvec3 v - Input vector.
dvec3 tangent - Return tangent vector.
dvec3 binormal - Return binormal vector.

void OrthoTransform ( vec3 v, mat4 transform ) #

Creates an ortho transformation. The transformation will be put to the transformation matrix.

Arguments

vec3 v - Input vector.
mat4 transform - Transformation matrix (mat4) to be set.

void OrthoTransform ( dvec3 v, dmat4 transform ) #

Creates an ortho transformation. The transformation will be put to the transformation matrix.

Arguments

dvec3 v - Input vector.
dmat4 transform - Transformation matrix (dmat4) to be set.

quat OrthoTangent ( vec4 t, vec3 n ) #

Creates the ortho triangle tangent space basis.

Arguments

vec4 t - Tangent vector.
vec3 n - Normal vector.

Return value

Tangent basis.

quat OrthoTangent ( vec3 t, vec3 b, vec3 n ) #

Creates the ortho triangle tangent space basis.

Arguments

vec3 t - Tangent vector.
vec3 b - Binormal vector.
vec3 n - Normal vector.

Return value

Tangent basis.

float TriangleArea ( vec3 v0, vec3 v1, vec3 v2 ) #

Returns the triangle area.

Arguments

vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.

Return value

Triangle area.

double TriangleArea ( dvec3 v0, dvec3 v1, dvec3 v2 ) #

Returns the triangle area.

Arguments

dvec3 v0 - The first triangle vertex.
dvec3 v1 - The second triangle vertex.
dvec3 v2 - The third triangle vertex.

Return value

Triangle area.

vec3 TriangleNormal ( vec3 v0, vec3 v1, vec3 v2 ) #

Returns the triangle normal vector.

Arguments

vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.

Return value

Triangle normal vector.

dvec3 TriangleNormal ( dvec3 v0, dvec3 v1, dvec3 v2 ) #

Returns the triangle normal vector.

Arguments

dvec3 v0 - The first triangle vertex.
dvec3 v1 - The second triangle vertex.
dvec3 v2 - The third triangle vertex.

Return value

Triangle normal vector.

vec4 TrianglePlane ( vec3 v0, vec3 v1, vec3 v2 ) #

Returns the triangle plane.

Arguments

vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.

Return value

Triangle plane.

dvec4 TrianglePlane ( dvec3 v0, dvec3 v1, dvec3 v2 ) #

Returns the triangle plane.

Arguments

dvec3 v0 - The first triangle vertex.
dvec3 v1 - The second triangle vertex.
dvec3 v2 - The third triangle vertex.

Return value

Triangle plane.

vec4 TriangleTangent ( vec3 v0, vec3 v1, vec3 v2 ) #

Returns the triangle tangent space.

Arguments

vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.

Return value

Triangle tangent space vector.

vec4 TriangleTangent ( vec3 v0, vec3 v1, vec3 v2, vec2 t0, vec2 t1, vec2 t2, vec3 normal ) #

Returns the triangle tangent space.

Arguments

vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.
vec2 t0 - Tangent vector of the first triangle vertex.
vec2 t1 - Tangent vector of the second triangle vertex.
vec2 t2 - Tangent vector of the third triangle vertex.
vec3 normal - Normal.

Return value

Triangle tangent space vector.

vec4 TriangleTangent ( vec3 v0, vec3 v1, vec3 v2, vec2 t0, vec2 t1, vec2 t2 ) #

Returns the triangle tangent space.

Arguments

vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.
vec2 t0 - Tangent vector of the first triangle vertex.
vec2 t1 - Tangent vector of the second triangle vertex.
vec2 t2 - Tangent vector of the third triangle vertex.

Return value

Triangle tangent space vector.

dvec4 PolygonPlane ( dvec3[] vertex, int[] indices ) #

Returns the polygon plane.

Arguments

dvec3[] vertex - Vertex structure.
int[] indices - Array of vertex indices.

Return value

Polygon plane.

vec4 PolygonPlane ( vec3[] vertex, int[] indices ) #

Returns the polygon plane.

Arguments

vec3[] vertex - Vertex structure.
int[] indices - Array of vertex indices.

Return value

Polygon plane.

bool PointTriangleInside ( vec3 point, vec3 v0, vec3 v1, vec3 v2 ) #

Checks if a point is inside a triangle.

Arguments

vec3 point - Point to be checked.
vec3 v0 - The first vertex of the triangle.
vec3 v1 - The second vertex of the triangle.
vec3 v2 - The third vertex of the triangle.

Return value

true if the point is inside the given triangle; otherwise, false.

bool PointTriangleInside ( dvec3 point, dvec3 v0, dvec3 v1, dvec3 v2 ) #

Checks if a point is inside a triangle.

Arguments

dvec3 point - Point to be checked.
dvec3 v0 - The first vertex of the triangle.
dvec3 v1 - The second vertex of the triangle.
dvec3 v2 - The third vertex of the triangle.

Return value

true if the point is inside the given triangle; otherwise, false.

bool PointTriangleInside ( vec3 point, vec3 v0, vec3 v1, vec3 v2, vec3 normal ) #

Checks if a point is inside a triangle.

Arguments

vec3 point - Point to be checked.
vec3 v0 - The first vertex of the triangle.
vec3 v1 - The second vertex of the triangle.
vec3 v2 - The third vertex of the triangle.
vec3 normal - Normal to the triangle plane.

Return value

true if the point is inside the given triangle; otherwise, false.

bool PointTriangleInside ( dvec3 point, dvec3 v0, dvec3 v1, dvec3 v2, dvec3 normal ) #

Checks if a point is inside a triangle.

Arguments

dvec3 point - Point to be checked.
dvec3 v0 - The first vertex of the triangle.
dvec3 v1 - The second vertex of the triangle.
dvec3 v2 - The third vertex of the triangle.
dvec3 normal - Normal to the triangle plane.

Return value

true if the point is inside the given triangle; otherwise, false.

float PointTriangleDistance ( vec3 point, vec3 v0, vec3 v1, vec3 v2, vec4 plane ) #

Returns the closest distance from a point to a triangle.

Arguments

vec3 point - Point.
vec3 v0 - The first vertex of the triangle.
vec3 v1 - The second vertex of the triangle.
vec3 v2 - The third vertex of the triangle.
vec4 plane - Triangle plane.

Return value

Distance.

double PointTriangleDistance ( dvec3 point, dvec3 v0, dvec3 v1, dvec3 v2, dvec4 plane ) #

Returns the closest distance from a point to a triangle.

Arguments

dvec3 point - Point.
dvec3 v0 - The first vertex of the triangle.
dvec3 v1 - The second vertex of the triangle.
dvec3 v2 - The third vertex of the triangle.
dvec4 plane - Triangle plane.

Return value

Distance.

void PointTriangleCoordinates ( vec2 point, vec2 v0, vec2 v1, vec2 v2, float a, float b ) #

Calculates barycentric triangle coordinates. The coordinates will be put to corresponding return variables.

Arguments

vec2 point - Point.
vec2 v0 - The first vertex of the triangle.
vec2 v1 - The second vertex of the triangle.
vec2 v2 - The third vertex of the triangle.
float a - Return variable.
float b - Return variable.

void PointTriangleCoordinates ( vec3 point, vec3 v0, vec3 v1, vec3 v2, float a, float b ) #

Calculates barycentric triangle coordinates. The coordinates will be put to corresponding return variables.

Arguments

vec3 point - Point.
vec3 v0 - The first vertex of the triangle.
vec3 v1 - The second vertex of the triangle.
vec3 v2 - The third vertex of the triangle.
float a - Return variable.
float b - Return variable.

void PointTriangleCoordinates ( dvec3 point, dvec3 v0, dvec3 v1, dvec3 v2, double a, double b ) #

Calculates barycentric triangle coordinates. The coordinates will be put to corresponding return variables.

Arguments

dvec3 point - Point.
dvec3 v0 - The first vertex of the triangle.
dvec3 v1 - The second vertex of the triangle.
dvec3 v2 - The third vertex of the triangle.
double a - Return variable.
double b - Return variable.

float PointPolygonDistance ( vec3 point, vec3[] vertex, int[] indices, vec4 plane ) #

Returns the distance from a point to a polygon.

Arguments

vec3 point - Point.
vec3[] vertex - Vertex structure.
int[] indices - Array of vertex indices.
vec4 plane - Polygon plane.

Return value

Distance.

double PointPolygonDistance ( dvec3 point, dvec3[] vertex, int[] indices, dvec4 plane ) #

Returns the distance from a point to a polygon.

Arguments

dvec3 point - Point.
dvec3[] vertex - Vertex structure.
int[] indices - Array of vertex indices.
dvec4 plane - Polygon plane.

Return value

Distance.

bool RayBoundBoxIntersection ( vec3 point, vec3 direction, vec3 min, vec3 max ) #

Checks if a ray intersects a bounding box. The same function as IRayBoundBoxIntersection(), but the latter has higher performance due to reduction of division operations, as the ray direction is replaced by the pre-calculated inverse of the ray direction.

Arguments

vec3 point - Starting point of the ray.
vec3 direction - Direction of the ray.
vec3 min - Min coordinates of the axis-aligned bounding box.
vec3 max - Max coordinates of the axis-aligned bounding box.

Return value

true if the given ray intersects the given bounding box; otherwise, false.

bool RayBoundBoxIntersection ( dvec3 point, dvec3 direction, dvec3 min, dvec3 max ) #

Arguments

dvec3 point - Starting point of the ray.
dvec3 direction - Direction of the ray.
dvec3 min - Min coordinates of the axis-aligned bounding box.
dvec3 max - Max coordinates of the axis-aligned bounding box.

Return value

true if the given ray intersects the given bounding box; otherwise, false.

bool IRayBoundBoxIntersection ( vec3 point, vec3 idirection, vec3 min, vec3 max ) #

Checks if there is an intersection between a ray and a bounding box. The same function as RayBoundBoxIntersection(), but it uses the inverse of the ray direction, which increases performance.

Arguments

vec3 point - Starting point of the ray.
vec3 idirection - Inverse direction of the ray.
vec3 min - Min coordinates of the axis-aligned bounding box.
vec3 max - Max coordinates of the axis-aligned bounding box.

Return value

true if the given ray intersects the given bounding box; otherwise, false.

bool IRayBoundBoxIntersection ( dvec3 point, dvec3 idirection, dvec3 min, dvec3 max ) #

Checks if there is an intersection between a ray and a bounding box. The same function as RayBoundBoxIntersection(), but it uses the inverse of the ray direction, which increases performance.

Arguments

dvec3 point - Starting point of the ray.
dvec3 idirection - Inverse direction of the ray.
dvec3 min - Min coordinates of the axis-aligned bounding box.
dvec3 max - Max coordinates of the axis-aligned bounding box.

Return value

true if the given ray intersects the given bounding box; otherwise, false.

bool RayTriangleIntersection ( vec3 point, vec3 direction, vec3 v0, vec3 v1, vec3 v2 ) #

Checks if a ray intersects a triangle.

Arguments

vec3 point - Starting point of the ray.
vec3 direction - Direction of the ray.
vec3 v0 - The first triangle vertex.
vec3 v1 - The second triangle vertex.
vec3 v2 - The third triangle vertex.

Return value

true if the given ray intersects the given triangle; otherwise, false.

bool RayTriangleIntersection ( dvec3 point, dvec3 direction, dvec3 v0, dvec3 v1, dvec3 v2 ) #

Checks if a ray intersects a triangle.

Arguments

dvec3 point - Starting point of the ray.
dvec3 direction - Direction of the ray.
dvec3 v0 - The first triangle vertex.
dvec3 v1 - The second triangle vertex.
dvec3 v2 - The third triangle vertex.

Return value

true if the given ray intersects the given triangle; otherwise, false.

bool LinePlaneIntersection ( vec3 p0, vec3 p1, vec4 plane ) #

Checks if there is an intersection between a line and a plane.