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Math3D Class

Provides helper methods for 3D math operations such as vector symmetry, orthogonal projection, plane projection, and line dash dissection.
Inheritance Hierarchy
SystemObject
  Altaxo.GeometryMath3D

Namespace: Altaxo.Geometry
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)
Syntax
C#
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public static class Math3D

The Math3D type exposes the following members.

Methods
 NameDescription
Public methodStatic memberDissectStraightLineWithDashPattern Dissects a straight line into individual line segments, using a dash pattern.
Public methodStatic memberGet2DProjectionToPlane Creates a transformation matrix that projects 2D points (represented as 3D points with ignored z-coordinate) to a plane defined by vectors e and n and a point p. The x-coordinate is projected in the e direction, the y-coordinate in the n direction.
Public methodStatic memberGet2DProjectionToPlaneToPlane Creates a transformation matrix that first maps a 2D point into a 3D coordinate system with origin p, and unit vectors e and n, then projects the created 3D point in the direction of v onto a plane defined by point p and the plane's normal q.
Public methodStatic memberGetDistancePointToPlane Gets the signed distance of a point a to a plane defined by a point p and a normal vector q. The distance is positive if the point a lies in the half-space into which q points.
Public methodStatic memberGetFractionalIndexOfPointOnLineInGivenDistanceToAnotherPoint Gets the fractional index of the point on a line that has a certain distance to another point ps.
Public methodStatic memberGetNormalizedVectorOrthogonalToVector Makes a given vector n orthogonal to another vector v and normalizes the result.
Public methodStatic memberGetProjectionToPlane Gets a projection matrix that projects a point in the direction given by v onto a plane defined by an arbitrary point on the plane p and the plane's normal q.
Public methodStatic memberGetRelativePositionsOnLineSegmentForPointsAtDistanceToPoint Gets the relative positions of the two points on a line segment that have a given distance to a third point. Returned values may be outside [0,1], and if no solution exists the values are NaN.
Public methodStatic memberGetVectorOrthogonalToVector Makes a given vector n orthogonal to another vector v by subtracting a fraction of v from n.
Public methodStatic memberGetVectorSymmetricalToPlane Calculates a vector which is symmetrical to the provided vector n with respect to the symmetry plane given by the normal q. The result corresponds to reflecting a ray on a mirror described by the plane.
Public methodStatic memberGetVectorSymmetricalToVector Calculates the counterpart of the provided vector n, so that this vector n and its counterpart are symmetrical, with the symmetry line provided by vector q.
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