Class GeometryUtils

Utility methods for common geometric operations

Inheritance

Object

GeometryUtils

Inherited Members

Object.ToString()

Object.Equals(Object)

Object.Equals(Object, Object)

Object.ReferenceEquals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Namespace: Unity.XR.CoreUtils

Syntax

public static class GeometryUtils

Methods

ClosestPointOnLineSegment(Vector3, Vector3, Vector3)

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

ClosestPointsOnTwoLineSegments(Vector3, Vector3, Vector3, Vector3, out Vector3, out Vector3, Double)

Finds the points along two line segments which are closest together

Declaration

public static bool ClosestPointsOnTwoLineSegments(Vector3 a, Vector3 aLineVector, Vector3 b, Vector3 bLineVector, out Vector3 resultA, out Vector3 resultB, double parallelTest = 4.94065645841247E-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	The resulting point along segment A
Vector3	resultB	The resulting point along segment B
Double	parallelTest	(Optional) epsilon value for parallel lines test

Returns

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

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

Find the closest points on the perimeter of a pair of polygons

Declaration

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

Parameters

Type	Name	Description
List<Vector3>	verticesA	The vertex list of polygon A
List<Vector3>	verticesB	The vertex list of polygon B
Vector3	pointA	The point on polygon A's closest to an edge of polygon B
Vector3	pointB	The point on polygon B's closest to an edge of polygon A
Single	parallelTest	The minimum distance between closest approaches used to detect parallel line segments

ClosestTimesOnTwoLines(Vector3, Vector3, Vector3, Vector3, out Single, out Single, Double)

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.

Declaration

public static bool ClosestTimesOnTwoLines(Vector3 positionA, Vector3 velocityA, Vector3 positionB, Vector3 velocityB, out float s, out float t, double parallelTest = 4.94065645841247E-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
Single	s	The time along trajectory a
Single	t	The time along trajectory b
Double	parallelTest	(Optional) epsilon value for parallel lines test

Returns

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

ClosestTimesOnTwoLinesXZ(Vector3, Vector3, Vector3, Vector3, out Single, out Single, Double)

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. This function ignores the y components.

Declaration

public static bool ClosestTimesOnTwoLinesXZ(Vector3 positionA, Vector3 velocityA, Vector3 positionB, Vector3 velocityB, out float s, out float t, double parallelTest = 4.94065645841247E-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
Single	s	The time along trajectory a
Single	t	The time along trajectory b
Double	parallelTest	(Optional) epsilon value for parallel lines test

Returns

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

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

Finds the smallest convex polygon in the xz plane that contains points Based on algorithm outlined in https://www.bitshiftprogrammer.com/2018/01/gift-wrapping-convex-hull-algorithm.html

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 values of these points are ignored.
List<Vector3>	hull	List that will be filled out with vertices that define a convex polygon

Returns

Type	Description
Boolean	True if points has at least 3 entries, false otherwise

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	The vertices that make up the bounds of the polygon. These must be convex but can be in either winding order.

Returns

Type	Description
Single	The area of the polygon

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

Finds the two closest adjacent vertices in a polygon, to a separate 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	An outline of a polygon defined by vertices, each one connected to the next
Vector3	point	The position in space to find the two closest outline vertices to
Vector3	vertexA	One vertex of the nearest edge
Vector3	vertexB	The other vertex of the nearest edge

Returns

Type	Description
Boolean	True if a nearest edge could be found

OrientedMinimumBoundingBox2D(List<Vector3>, Vector3[])

Find the oriented minimum bounding box for a 2D convex hull. This implements the 'rotating calipers' algorithm and operates in linear time. Operates only on the X and Z axes of the input.

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

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	The vertices that make up the bounds of the polygon

Returns

Type	Description
Boolean	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	The vertices that make up the bounds of the polygon, these should be convex and coplanar but can have any normal

Returns

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

PointOnLineSegmentXZ(Vector3, Vector3, Vector3, Single)

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 = 1.401298E-45F)

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
Single	epsilon	Custom epsilon value used for comparison checks

Returns

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

PointOnOppositeSideOfPolygon(List<Vector3>, Vector3)

Finds the furthest intersection point on a polygon from a point in space

Declaration

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

Parameters

Type	Name	Description
List<Vector3>	vertices	An outline of a polygon defined by vertices, each one connected to the next
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

PointOnPolygonBoundsXZ(Vector3, List<Vector3>, Single)

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 = 1.401298E-45F)

Parameters

Type	Name	Description
Vector3	testPoint	The point to test
List<Vector3>	vertices	The vertices that make up the bounds of the polygon
Single	epsilon	Custom epsilon value used when testing if the point lies on an edge

Returns

Type	Description
Boolean	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	The vertices of the 2D polygon

Returns

Type	Description
Vector3	The centroid point for the polygon

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

Determines if one polygon lies completely inside a 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
Boolean	True if polygonA lies completely inside polygonB, false otherwise

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

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
Single	maxDistance	The maximum distance allowed between the two polygons

Returns

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

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

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 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
Single	maxSqDistance	The square of the maximum distance allowed between the two polygons

Returns

Type	Description
Boolean	True if the polygons are within the specified distance from each other, 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.

ProjectPointOnPlane(Vector3, Vector3, Vector3)

Returns the closest point on a plane to another point

Declaration

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

Parameters

Type	Name	Description
Vector3	planeNormal	The plane normal
Vector3	planePoint	A point on the plane
Vector3	point	The other point

Returns

Type	Description
Vector3	The closest point on the plane to the other 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<Int32>, Int32, Boolean)

Given a number of perimeter vertices, generate a triangle buffer and add it to the given list The winding order is reversible. Example winding orders: Normal: Reverse: 0, 1, 2, 0, 2, 1, 0, 2, 3, 0, 3, 2, 0, 3, 4, 0, 4, 3, --etc--

Declaration

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

Parameters

Type	Name	Description
List<Int32>	indices	The list to which the triangle buffer will be added
Int32	vertCount	The number of perimeter vertices
Boolean	reverse	(Optional) Whether to reverse the winding order of the vertices