clipping

Intro

The clipping is implemented on the Linked Simplex data structure. The Clipping Theory describes the algorithm and how it uses the data structure to clip simplexes.

Discussion

What was interesting for me was that clipping is neither straight forward or well defined but subjective. For example a boundary of points may need to be interpreted into an analytical curve, or as a polyline but vary which points on the polyline are used. This is a vast subject so I will just say what I did.

Rather than define a generic subtraction of one mesh from another a subtraction of a partition from a mesh was defined. This alows for analytic partitions to be subtracted from the mesh. For example subtracting a circle from a 2D mesh.

This resulted in the partition having an interface which supported asking if a point was inside the partition, if a point was on the boundary, and surprisingly given two points on opposite sides of the partition interpolate the intersection point. This operation make sense as the simplex goes to zero (becomes smaller) which is really the mesh becomming a finer grain calculate a point on the boundary.

Source

Files

Doxygen

TODO

• Object orientated program: the main should call objects and contain no code, fix.
• Redo rotation and translation to use d2homogenous in mathlib.h
• menu for keyboard options
• Mesh subtraction in 2D by deriving from a partition.
• Clipping in 3D
• Rotation default about origin. Extend logic to include rotation about any point. if A is rotation matrix, x the point and p0 the rotation point, x = A(x-p0) + p0