Class GeometryUtils

Utility methods for common geometric operations.

Inheritance

object

GeometryUtils

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: Unity.XR.CoreUtils

Assembly: Unity.XR.CoreUtils.dll

Syntax

public static class GeometryUtils

Methods

ClosestPointOnLineSegment(Vector3, Vector3, Vector3)

Returns the point along a line segment closest to a given point.

Declaration

public static Vector3 ClosestPointOnLineSegment(Vector3 point, Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	point	The point to test against the line segment.
Vector3	a	The first point of the line segment.
Vector3	b	The second point of the line segment.

Returns

Type	Description
Vector3	The point along the line segment closest to point.

ClosestPointsOnTwoLineSegments(Vector3, Vector3, Vector3, Vector3, out Vector3, out Vector3, double)

Finds the closest points between two line segments.

Declaration

public static bool ClosestPointsOnTwoLineSegments(Vector3 a, Vector3 aLineVector, Vector3 b, Vector3 bLineVector, out Vector3 resultA, out Vector3 resultB, double parallelTest = 5E-324)

Parameters

Type	Name	Description
Vector3	a	Starting point of segment A.
Vector3	aLineVector	Vector from point a to the end point of segment A.
Vector3	b	Starting point of segment B.
Vector3	bLineVector	Vector from point b to the end point of segment B.
Vector3	resultA	Set to the coordinates of the point along segment A that is closest to any point on segment B.
Vector3	resultB	Set to the coordinates of the point along segment B that is closest to any point on segment A.
double	parallelTest	(Optional) epsilon value for parallel lines test

Returns

Type	Description
bool	True if the line segments are parallel, false otherwise

Remarks

If the two line segments are parallel, then resultA and resultB are set to the midpoint of the respective line segments.

ClosestPolygonApproach(List<Vector3>, List<Vector3>, out Vector3, out Vector3, float)

Finds the closest points of the perimeters of two polygons.

Declaration

public static void ClosestPolygonApproach(List<Vector3> verticesA, List<Vector3> verticesB, out Vector3 pointA, out Vector3 pointB, float parallelTest = 0)

Parameters

Type	Name	Description
List<Vector3>	verticesA	Vertices defining the outline of polygon A.
List<Vector3>	verticesB	Vertices defining the outline of polygon B.
Vector3	pointA	The point on polygon A closest to an edge of polygon B.
Vector3	pointB	The point on polygon B closest to an edge of polygon A.
float	parallelTest	The minimum distance between closest approaches used to detect parallel line segments.

ClosestTimesOnTwoLines(Vector3, Vector3, Vector3, Vector3, out float, out float, double)

Finds the times at which two linear trajectories are the closest to each other.

Declaration

public static bool ClosestTimesOnTwoLines(Vector3 positionA, Vector3 velocityA, Vector3 positionB, Vector3 velocityB, out float s, out float t, double parallelTest = 5E-324)

Parameters

Type	Name	Description
Vector3	positionA	Starting point of object a
Vector3	velocityA	Velocity (direction and magnitude) of object a
Vector3	positionB	Starting point of object b
Vector3	velocityB	Velocity (direction and magnitude) of object b
float	s	The time along trajectory a
float	t	The time along trajectory b
double	parallelTest	(Optional) epsilon value for parallel lines test

Returns

Type	Description
bool	False if the lines are parallel, otherwise true

Remarks

Two trajectories which may or may not intersect have a time along each path which minimizes the distance between trajectories. This function finds those two times. The same logic applies to line segments, where the one point is the starting position, and the second point is the position at t = 1.

ClosestTimesOnTwoLinesXZ(Vector3, Vector3, Vector3, Vector3, out float, out float, double)

Finds the times of closest approach between two non-parallel trajectories.

Declaration

public static bool ClosestTimesOnTwoLinesXZ(Vector3 positionA, Vector3 velocityA, Vector3 positionB, Vector3 velocityB, out float s, out float t, double parallelTest = 5E-324)

Parameters

Type	Name	Description
Vector3	positionA	Starting point of object A.
Vector3	velocityA	Velocity (direction and magnitude) of object A.
Vector3	positionB	Starting point of object B.
Vector3	velocityB	Velocity (direction and magnitude) of object B.
float	s	Set to the calculated time of closest approach along trajectory A.
float	t	Set to the calculated time of closest approach along trajectory B.
double	parallelTest	(Optional) A custom epsilon value for teh parallel lines test.

Returns

Type	Description
bool	False if the lines are parallel, otherwise true.

Remarks

Two trajectories, which may or may not intersect, have a time along each path that minimizes the distance between trajectories. This function finds those two times. The same logic applies to line segments, where the one point is the starting position, and the second point is the position at t = 1. This function ignores the y components.

ConvexHull2D(List<Vector3>, List<Vector3>)

Finds the smallest convex polygon in the XZ plane that contains points.

Declaration

public static bool ConvexHull2D(List<Vector3> points, List<Vector3> hull)

Parameters

Type	Name	Description
List<Vector3>	points	Points used to find the convex hull. The y coordinates of these points are ignored.
List<Vector3>	hull	The vertices that define the smallest convex polygon are assigned to this list. The list is not cleared.

Returns

Type	Description
bool	True if points has at least 3 elements, false otherwise.

Remarks

Based on algorithm outlined in Gift Wrapping Convex Hull Algorithm With Unity Implementation.

ConvexPolygonArea(List<Vector3>)

Finds the area of a convex polygon.

Declaration

public static float ConvexPolygonArea(List<Vector3> vertices)

Parameters

Type	Name	Description
List<Vector3>	vertices	Vertices defining the outline of a polygon. The polygon must be convex, but can be in either winding order.

Returns

Type	Description
float	The area of the polygon.

FindClosestEdge(List<Vector3>, Vector3, out Vector3, out Vector3)

Finds the side of a polygon closest to a specified world space position.

Declaration

public static bool FindClosestEdge(List<Vector3> vertices, Vector3 point, out Vector3 vertexA, out Vector3 vertexB)

Parameters

Type	Name	Description
List<Vector3>	vertices	Vertices defining the outline of a polygon.
Vector3	point	The position in space to find the two closest outline vertices to.
Vector3	vertexA	The coordinates of the first vertex of the nearest side is assigned to this out parameter.
Vector3	vertexB	The coordinates of the second vertex of the nearest side is assigned to this out parameter.

Returns

Type	Description
bool	True if a nearest edge could be found.

OrientedMinimumBoundingBox2D(List<Vector3>, Vector3[])

Find the oriented minimum bounding box for a 2D convex hull.

Declaration

public static Vector2 OrientedMinimumBoundingBox2D(List<Vector3> convexHull, Vector3[] boundingBox)

Parameters

Type	Name	Description
List<Vector3>	convexHull	The list of all points in a 2D convex hull on the X and Z axes, in a clockwise winding order.
Vector3[]	boundingBox	An array of length 4 to fill with the vertex positions of the bounding box, in the order { top left, bottom left, bottom right, top right }.

Returns

Type	Description
Vector2	The size of the bounding box on each axis. Y here maps to the Z axis.

Remarks

This implements the 'rotating calipers' algorithm and operates in linear time. Operates only on the X and Z axes of the input.

PointInPolygon(Vector3, List<Vector3>)

Determines if a point is inside of a polygon on the XZ plane. (The y value is not used.)

Declaration

public static bool PointInPolygon(Vector3 testPoint, List<Vector3> vertices)

Parameters

Type	Name	Description
Vector3	testPoint	The point to test.
List<Vector3>	vertices	Vertices defining the outline of a polygon.

Returns

Type	Description
bool	True if the point is inside the polygon, false otherwise.

PointInPolygon3D(Vector3, List<Vector3>)

Determines if a point is inside of a convex polygon and lies on the surface.

Declaration

public static bool PointInPolygon3D(Vector3 testPoint, List<Vector3> vertices)

Parameters

Type	Name	Description
Vector3	testPoint	The point to test.
List<Vector3>	vertices	Vertices defining the outline of the polygon. The polygon must be convex. The vertices must be coplanar, but can lie on any arbitrary plane.

Returns

Type	Description
bool	True if the point is inside the polygon and coplanar, false otherwise.

PointOnLineSegmentXZ(Vector3, Vector3, Vector3, float)

Determines if a point lies on a line segment, ignoring the y components.

Declaration

public static bool PointOnLineSegmentXZ(Vector3 testPoint, Vector3 lineStart, Vector3 lineEnd, float epsilon = 1E-45)

Parameters

Type	Name	Description
Vector3	testPoint	The point to test.
Vector3	lineStart	Starting point of the line segment.
Vector3	lineEnd	Ending point of the line segment.
float	epsilon	Custom epsilon value used for comparison checks.

Returns

Type	Description
bool	True if the point lies on the line segment, false otherwise.

PointOnOppositeSideOfPolygon(List<Vector3>, Vector3)

Finds the point on a polygon perimeter farthest from a specified point in space.

Declaration

public static Vector3 PointOnOppositeSideOfPolygon(List<Vector3> vertices, Vector3 point)

Parameters

Type	Name	Description
List<Vector3>	vertices	Vertices defining the outline of a polygon.
Vector3	point	The position in world space to find the furthest intersection point.

Returns

Type	Description
Vector3	A world space position of a point on the polygon that is as far from the input point as possible. Returns zero if vertices contains less than tree points.

PointOnPolygonBoundsXZ(Vector3, List<Vector3>, float)

Determines if a point lies on the bounds of a polygon, ignoring the y components.

Declaration

public static bool PointOnPolygonBoundsXZ(Vector3 testPoint, List<Vector3> vertices, float epsilon = 1E-45)

Parameters

Type	Name	Description
Vector3	testPoint	The point to test.
List<Vector3>	vertices	Vertices defining the outline of a polygon.
float	epsilon	Custom epsilon value used when testing if the point lies on an edge.

Returns

Type	Description
bool	True if the point lies on any edge of the polygon, false otherwise.

PolygonCentroid2D(List<Vector3>)

Given a list of vertices of a 2d convex polygon, find the centroid of the polygon. This implementation operates only on the X and Z axes.

Declaration

public static Vector3 PolygonCentroid2D(List<Vector3> vertices)

Parameters

Type	Name	Description
List<Vector3>	vertices	Vertices defining the outline of a 2D polygon.

Returns

Type	Description
Vector3	The centroid point for the polygon.

PolygonInPolygon(List<Vector3>, List<Vector3>)

Determines if one polygon lies completely inside another coplanar polygon.

Declaration

public static bool PolygonInPolygon(List<Vector3> polygonA, List<Vector3> polygonB)

Parameters

Type	Name	Description
List<Vector3>	polygonA	The polygon to test for lying inside polygonB.
List<Vector3>	polygonB	The polygon to test for containing polygonA. Must be convex and coplanar with polygonA.

Returns

Type	Description
bool	True if polygonA lies completely inside polygonB, false otherwise.

PolygonUVPoseFromPlanePose(Pose)

Gets a corrected polygon uv pose from a given plane pose.

Declaration

public static Pose PolygonUVPoseFromPlanePose(Pose pose)

Parameters

Type	Name	Description
Pose	pose	The source plane pose.

Returns

Type	Description
Pose	The rotation-corrected pose for calculating UVs.

PolygonVertexToUV(Vector3, Pose, Pose)

Takes a polygon UV coordinate, and produces a pose-corrected UV coordinate.

Declaration

public static Vector2 PolygonVertexToUV(Vector3 vertexPos, Pose planePose, Pose uvPose)

Parameters

Type	Name	Description
Vector3	vertexPos	Vertex to transform.
Pose	planePose	Polygon pose.
Pose	uvPose	UV-correction Pose.

Returns

Type	Description
Vector2	The corrected UV coordinate.

PolygonsWithinRange(List<Vector3>, List<Vector3>, float)

Determines if two convex coplanar polygons are within a certain distance from each other. This includes the polygon perimeters as well as their interiors.

Declaration

public static bool PolygonsWithinRange(List<Vector3> polygonA, List<Vector3> polygonB, float maxDistance)

Parameters

Type	Name	Description
List<Vector3>	polygonA	The first polygon to test. Must be convex and coplanar with polygonB.
List<Vector3>	polygonB	The second polygon to test. Must be convex and coplanar with polygonA.
float	maxDistance	The maximum distance allowed between the two polygons.

Returns

Type	Description
bool	True if the polygons are within the specified distance from each other, false otherwise.

PolygonsWithinSqRange(List<Vector3>, List<Vector3>, float)

Determines if two convex coplanar polygons are within a specified distance from each other.

Declaration

public static bool PolygonsWithinSqRange(List<Vector3> polygonA, List<Vector3> polygonB, float maxSqDistance)

Parameters

Type	Name	Description
List<Vector3>	polygonA	The first polygon to test. Must be convex and coplanar with polygonB.
List<Vector3>	polygonB	The second polygon to test. Must be convex and coplanar with polygonA.
float	maxSqDistance	The square of the maximum distance allowed between the two polygons.

Returns

Type	Description
bool	True if the polygons are within the specified distance from each other, false otherwise.

ProjectPointOnPlane(Vector3, Vector3, Vector3)

Returns the point on a plane closest to a specified point.

Declaration

public static Vector3 ProjectPointOnPlane(Vector3 planeNormal, Vector3 planePoint, Vector3 point)

Parameters

Type	Name	Description
Vector3	planeNormal	The plane normal. (It does not need to be normalized.)
Vector3	planePoint	Any point on the plane.
Vector3	point	The point to test.

Returns

Type	Description
Vector3	The point on the plane closest to point.

RotationForBox(Vector3[])

Given a 2D bounding box's vertices, find the rotation of the box.

Declaration

public static Quaternion RotationForBox(Vector3[] vertices)

Parameters

Type	Name	Description
Vector3[]	vertices	The 4 vertices of the bounding box, in the order { top left, bottom left, bottom right, top right }.

Returns

Type	Description
Quaternion	The rotation of the box, with the horizontal side aligned to the x axis and the vertical side aligned to the z axis

TriangulatePolygon(List<int>, int, bool)

Generates a standard triangle buffer with a given number of indices and adds it to the specified list.

Declaration

public static void TriangulatePolygon(List<int> indices, int vertCount, bool reverse = false)

Parameters

Type	Name	Description
List<int>	indices	The list to which to add the triangle buffer. The list is not cleared.
int	vertCount	The number of perimeter vertices.
bool	reverse	(Optional) Whether to reverse the winding order of the vertices.

Remarks

Set reverse true to reverse the normal winding order.

Example winding orders:

Normal winding	Reverse winding
0, 1, 2,	0, 2, 1,
0, 2, 3,	0, 3, 2,
0, 3, 4,	0, 4, 3,
...	...