A Primer on Bézier Curves. A free, online book for when you really need to know how to do Bézier things
Источник: https://pomax.github.io/bezierinfo/
| QUOTE | Main content
A lightning introduction
So what makes a Bézier Curve?
The mathematics of Bézier curves
Controlling Bézier curvatures
Controlling Bézier curvatures, part 2: Rational Béziers
The Bézier interval [0,1]
Bézier curvatures as matrix operations
de Casteljau's algorithm
Simplified drawing
Splitting curves
Splitting curves using matrices
Lowering and elevating curve order
Derivatives
Tangents and normals
Working with 3D normals
Component functions
Finding extremities: root finding
Bounding boxes
Aligning curves
Tight bounding boxes
Curve inflections
The canonical form (for cubic curves)
Finding Y, given X
Arc length
Approximated arc length
Curvature of a curve
Tracing a curve at fixed distance intervals
Intersections
Curve/curve intersection
The projection identity
Creating a curve from three points
Projecting a point onto a Bézier curve
Molding a curve
Curve fitting
Bézier curves and Catmull-Rom curves
Creating a Catmull-Rom curve from three points
Forming poly-Bézier curves
Curve offsetting
Graduated curve offsetting
Circles and quadratic Bézier curves
Circles and cubic Bézier curves
Approximating Bézier curves with circular arcs
B-Splines
Comments and questions
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