Module measure 

Bounding volumes and projection.

Bounds must contain what they claim to

A bounding box in a kernel is always a rejection test. Too large costs time; too small silently drops a real intersection, and nothing downstream can tell it happened. So every bound here is derived from a property that guarantees containment, never from sampling:

• a line’s bound is its endpoints, which is exact;
• a spline’s is its control points, which is guaranteed by the convex hull property: the curve never leaves the hull of its control polygon;
• an analytic curve or surface’s is computed from its own definition;
• a trimmed piece falls back to the bound of the whole, which is loose but never wrong.

Sampling a curve at a few parameters and taking the extremes is the obvious alternative and is not sound: the curve bulges between the samples, and the amount it bulges is exactly what a bound is supposed to capture.

Structs

Obb

A box that has been turned to fit what it bounds.

Projection

Where a point projects onto a curve, and how far away it is.

SurfaceProjection

Where a point projects onto a surface.

SurfaceSeeds

A surface’s seeding grid, built once and asked many times.

Functions

curve_bounds

A guaranteed bound for a space curve.

curve_bounds_over

A guaranteed bound for the part of a curve an edge actually uses.

face_normal

The direction a face presents, in space.

oriented_bounds

An oriented bound for a shape, from the spread of its geometry.

project_on_curve

The nearest point on a curve to target.

project_on_planar_curve

The nearest point on a planar curve to a point in the same parameter space.

project_on_surface

The nearest point on a surface to target.

project_on_surface_from

The nearest point on a surface to target, starting from a guess.

relative_deflection

A deflection expressed as a fraction of a shape’s own size.

shape_bounds

A guaranteed bound for a shape, including everything below it.

surface_bounds

A guaranteed bound for a surface.

vertex_bounds

A bound for a shape built only from its vertices.

widened_to_hold

A surface’s parameterization window widened until it holds every one of points.