نيربس
نـِربس (NURBS:Non-uniform rational basis spline ) هونموذج رياضي شاع استخدامة في رسومات الكمبيوتر لتوليد وتمثيل منحنيات وسطوح والذي يقدم قدر كبير من الدقة والمرونة في التعامل معه سواء بالكيفية التحليلية اوبانشاء أشكال حرة (free form).
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التاريخ
الاستخدام
إنشاء دوال الأساس
rises linearly from zero to one on the interval where is non-zero, while falls from one to zero on the interval where is non-zero. As mentioned before, is a triangular function, nonzero over two knot spans rising from zero to one on the first, and falling to zero on the second knot span. Higher order basis functions are non-zero over corresponding more knot spans and have correspondingly higher degree. If is the parameter, and is the -th knot, we can write the functions and as
و
The functions
الشكل العام لمنحنى نربس
Using the definitions of the basis functions from the previous paragraph, a NURBS curve takes the following form:
In this, is the number of control points and are the corresponding weights. The denominator is a normalizing factor that evaluates to one if all weights are one. This can be seen from the partition of unity property of the basis functions. It is customary to write this as
in which the functions
are known as the rational basis functions.
انظر أيضاً
- Spline
- de Boor's algorithm
- Subdivision surface
- Triangle mesh
- Point cloud
- Rational motion
- Isogeometric analysis
الهامش
- ^ Les Piegl & Wayne Tiller: The NURBS Book, chapter 2, sec. 2
- ^ Les Piegl & Wayne Tiller: The NURBS Book, chapter 4, sec. 2
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