Intersection algorithm for two B-spline curves using Bézier clipping

Find intersection points between two B-spline curves

• Find intersection between one of (point, straight line, or curve) and one of (point, straight line, or curve).
• Each iteration info is saved in node_info.log file.
• Verbose info optionally can be saved in calc.log file.
• A curve should satisfy m = n + p + 1. (m: knot vector [u_0, u_m], n: control points [P_0, P_n], p: degree of a curve)
• Overlapping can be found by adjusting a level of accuracy resulting in a lot of binary subdivisions.

How to use

Interpolation mode

• A curve is supposed to pass through the selected points.
• Global interpolation is used. A curve becomes distorted as the degree of a curve is elevated.
• The same point cannot be selected successively, which causes an LU decomposition failure.
• The minimum number of interpolation points to make a curve is degree + 2.

Control points mode

• With the interpolation mode off, the selected points are control points of a curve.
• The minimum number of control points to make a curve is degree + 1.
• A point can be created by selecting the same point at least degree + 1 times.

Limitation

• Not for self intersection

Development Tools

• Microsoft Visual Studio Community 2022 (64-bit) - Version 17.12.0 Preview 2.1 C++latest(modules)

Library via vcpkg

• sfml:x64-windows 2.6.1
• imgui:x64-windows 1.91.0
• imgui-sfml:x64-windows 2.6
• magic-enum:x64-windows 0.9.6

Sample calculation