BezierCurve
BezierCurve[{pt1,pt2,…}]
is a graphics primitive that represents a Bézier curve with control points pti.
Details and Options
- BezierCurve can be used in both Graphics and Graphics3D (two‐ and three‐dimensional graphics).
- The positions of control points can be specified either in ordinary coordinates as {x,y} or {x,y,z}, or in scaled coordinates as Scaled[{x,y}] or Scaled[{x,y,z}].
- In two dimensions, Offset and ImageScaled can be used to specify coordinates.
- BezierCurve by default represents a composite cubic Bézier curve.
- SplineDegree->d specifies that the underlying polynomial basis should have maximal degree d.
- With SplineDegree->d, BezierCurve with d+1 control points yields a simple degree-d Bézier curve. With fewer control points, a lower-degree curve is generated. With more control points, a composite Bézier curve is generated. »
- Curve thickness can be specified using Thickness or AbsoluteThickness, as well as Thick and Thin. »
- Curve dashing can be specified using Dashing or AbsoluteDashing, as well as Dashed, Dotted, etc. »
- Curve shading or coloring can be specified using CMYKColor, GrayLevel, Hue, Opacity, or RGBColor. »
- Individual coordinates and lists of coordinates in BezierCurve can be Dynamic objects.
Examples
open allclose allBasic Examples (1)
Scope (11)
Curve Specification (4)
Curve Styling (4)
Coordinate Specification (3)
Generalizations & Extensions (3)
Applications (7)
Graphics, Glyphs, etc. (4)
Approximate a circle with 4 Bézier curves:
A quadratic Bézier curve can be converted into a cubic Bézier curve:
Define the outline of a glyph:
Use BezierCurve instead of lines to draw the edges:
Interpolation (1)
Choose 4 points to be interpolated:
Compute distances between control points:
Compute normalized parameters with respect to the distances (chord length parametrization):
Since a Bézier curve interpolates endpoints, you only need to compute two intermediate points:
Least Squares Fitting (1)
Properties & Relations (11)
A Bézier curve always interpolates the endpoints:
A Bézier curve with degree 1 is equivalent to Line:
A Bézier curve is affine invariant:
A single Bézier curve lies in the convex hull of the control points:
In 3D, a Bézier curve with planar control points lies in the plane:
The cubic Bernstein polynomials:
A Bézier curve can be constructed from the sum of the Bernstein polynomials:
A Bézier curve generated from the average of two sets of control points:
The new curve is indeed the average of two Bézier curves:
A composite Bézier curve may not be smooth at the point where two segments meet:
By making the adjacent points collinear, you can get a smooth composite Bézier curve:
A single BezierCurve is a special case of BSplineCurve:
In 3D, a single Bézier surface patch can be generated using BSplineSurface:
Text
Wolfram Research (2008), BezierCurve, Wolfram Language function, https://reference.wolfram.com/language/ref/BezierCurve.html.
CMS
Wolfram Language. 2008. "BezierCurve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BezierCurve.html.
APA
Wolfram Language. (2008). BezierCurve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BezierCurve.html