Computer Graphics. Curves and Surfaces. Hermite/Bezier Curves, (B-)Splines, and. NURBS. By. Ulf Assarsson. Most of the material is originally made by. Uniform cubic b-splines has C2 continuity. – Higher than Hermite or Bezier curves. Computer Graphics. 10/10/ Lecture 5. Basis Functions. Computer Graphics Curves - Learn about Computer Graphics in simple and easy terms Bezier curve is discovered by the French engineer Pierre Bézier.
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In computer graphics, a spline is a curve that connects two or more specific points, or that is defined by two or more points.
The term can also refer to the mathematical equation that defines such a curve. Consider the set of points in the illustration below.
Each point has two neighbors except endpoints. Implicit Curves Implicit curve representations define the set of points on a curve by employing a procedure that can test to see if a point in on the curve.
Such a function is the explicit representation of the curve. The explicit representation is not general, since it cannot represent vertical lines and is also single-valued.
Computer Graphics Curves
For each value of x, only a single value of y is normally computed by the function. Parametric Curves Curves having parametric form are called parametric curves. The explicit and implicit curve representations can be used only when the function is known.
In practice the parametric curves are used. These curves can be generated under the control of other points. OpenType fonts can use either kind, depending spline curve in computer graphics the flavor of the font.
B-spline - Wikipedia
The exact splitting algorithm is implementation dependent, only the flatness criteria must be respected to reach the necessary precision and to avoid non-monotonic local changes of curvature.
The "smooth curve" feature of charts in Microsoft Excel also uses this algorithm. This approach also allows preserving the curve definition under all linear or perspective 2D and 3D transforms and projections. The first and last control points are always the end points of the curve; however, the intermediate control points if any spline curve in computer graphics do not lie on the curve.