## V# main feature overview

V# comprises over 800 methods in over 15000 lines of code. The most important are:

## Spatial point, edge, line, plane, triangle, circle, ellipse and arc operations:

• Distances and perpendiculars between all supported objects
• Parallel projections of all supported objects
• Point reflection, reflection across a line, reflection through a plane of all supported objects
• Coordinate transformation, scaling, moving, arbitrary center rotation of all supported objects
• Tests: Intersection, containment, collinearity, coplanarity, overlap and other
• Triangle: barycentric and trilinear coordinates
• Triangle: slice by plane
• Triangle: many special points, circles and lines (e.g. in-, ex- and circumcircles, inscribed ellipse)
• Plane: analytic, coordinate, normal coordinate and parametric form
• Circles: construct from three points, tangents

## Pointsets

• 2d and 3d multiple point removal
• Orthogonal least square lines and planes
• High performance rotation, moving, coordinate transformation
• Random permutation
• Lexicographical sort
• ASCII file IO

## 3x3 Matrices

• Arbitrary, fixed and moving axes rotation matrices
• Cross product matrix, identity matrix
• Determinant, inverse, transpose, eigenvectors and eigenvalues
• Orthonormalization and orthogonalization
• Trace, norm
• Tests for symmetry, orthogonality, rotation and positive definite
• Linear system solver

## 4x4 matrices

• Determinant
• Linear system solver

## Vectors

• Dot, cross and tensor product
• Projection on plane/vector
• Normalization
• Rotation
• Coordinate transformation
• Angle between two vectors
• Bisecting vector of two vectors
• Parallelity and orthogonality test
• Test for linear independency

## DXF file output

• AC1009 format dxf export of all objects
• Additional text output
• All entities on user-definable layers
• Linetype, point display mode definition

## Others

• Golden section line search
• Random generator
• Kernel time gauge
• Coordinate transformation by four point in two systems ("align")

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