Shapes

Topics
	Basic shapes
	Basic shapes: circle and rectangle.
	CSG (Constructive Solid Geometry) shapes
	CSG operations: union, intersection and difference.
	Polygon shape
	Polygonal shape (2D only)
	Surface mesh shape
	Shape defined by a surface mesh (3D only)
	Abstract type shape
	Abstract definition of a shape.

Detailed Description

This group provides a way to define geometric shapes with a combination of:

• Geometric shapes: polygon, sphere, polygonal surface mesh, etc.
• Constructive Solid Geometry (CGS) operations: boolean operations on shapes (union, intersection, difference, inverse)
• Transformations: rotation, scaling, translation

Example of a shape defined by CSG operations:

               ┌───────────┐
               │   union   │
               └───────────┘
            ╭───────╯ ╰───────╮
            │                 │
  ┌────────────┐           ┌────────────┐
  │   circle   │           │ difference │
  └────────────┘           └────────────┘
                        ╭───────╯ ╰───────╮
                        │                 │
                   ┌───────────┐      ┌───────────┐
                   │  polygon  │      │ rectangle │
                   └───────────┘      └───────────┘

Every shape derived from the abstract type t_shape. Any shapes implements three operations:

• is_inside: Check if a given point lies inside the shape.

• get_samples_inside: Check if a sample of point in a given cell lies in the shape. The sampling level is driven by the n_samples parameter.

  Example of sampling for various sampling levels:

        n_samples = 0   n_samples = 1   n_samples = 2
          ┏━━━━━━━┓       ×━━━×━━━×       ×━×━×━×━×
          ┃       ┃       ┃       ┃       × × × × ×
          ┃   ×   ┃       ×   ×   ×       × × × × ×    ...
          ┃       ┃       ┃       ┃       × × × × ×
          ┗━━━━━━━┛       ×━━━×━━━×       ×━×━×━×━×

• get_distance: Compute the closest distance between a given point and the shape. It also compute the direction to the closest point.