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Math3D Class

[Missing <summary> documentation for "T:Altaxo.Geometry.Math3D"]

Inheritance Hierarchy
SystemObject
  Altaxo.GeometryMath3D

Namespace: Altaxo.Geometry
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
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 (in fact: 3D-points with ignored z-coordinate) to a plane that is defined by 2 vectors (e and n) and a point on that plane p. The x-coordinates of the original point is projected in the e direction, the y-coordinate in the n direction.
Public methodStatic memberGet2DProjectionToPlaneToPlane Creates a transformation matrix that does the following: First, it converts a 2D point into a 3D coordinate system with the origin given by p, and the unit vectors e and n. Then the thus created 3D point is projected in the direction of v onto a plane that is defined by the same point p on the plane and the plane's normal q.
Public methodStatic memberGetDistancePointToPlane Gets the distance of a point a to a plane defined by a point p and a normal vector q. The distance is considered to be positive if the point a is located in the half space into which the vector q is pointing.
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. This is done by adding a fraction of v to n, so that the new vector is orthogonal to v. After this, the vector is normalized.
Public methodStatic memberGetProjectionToPlane Gets a projection matrix that projects a point in the direction given by v onto a plane with is given 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. The returned relative values are in the range [-Infinity, Infinity] and therefore don't neccessarily lie directly on the line segment. Furthermore, a solution not always exists (in this case the returned values are NaN).
Public methodStatic memberGetVectorOrthogonalToVector Makes a given vector n orthogonal to another vector v. This is done by adding a fraction of v to n, so that the new vector is orthogonal to v.
Public methodStatic memberGetVectorSymmetricalToPlane Calculates a vector which is symmectrical to the provided vector n with respected to the symmetry plane given by the normal normal q. The result is the same as if a ray is reflected on a miiror described by the plane, thus an incident vector is resulting in an outcoming vector, and an outcoming vector is resulting in an incident vector.
Public methodStatic memberGetVectorSymmetricalToVector Calculates the counterpart of the provided vector n, so that this vector n and it's conterpart are symmetrical, with the symmetry line provided by vector q.
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