NURBS学习第一天

曲线和表面的基础

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隐式形式和参数形式（page1~5）

优缺点对比.

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The power basis and Bezier forms are mathematically equivalent.
However, the Bezier method is superior to the power basis form for geometric modeling.

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Power basis curve (page6)

C(u)=(x(u),y(u),z(u))=∑i=0naiui0⩽u⩽1

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Bezier Curves(page9)

C(u)=∑i=0nBi,n(u)Pi0⩽u⩽1

Bi,n(u)=n!i!(n−i)!ui(1−u)n−i

Bezier curves are invariant under the usual transformations such as rotations, translations, and scalings;that is, one applies the transformation to the curve by applying it to the control polygon Pi.
Bezier的算法算法实现（page20）

Bernstein(i,n,u,B){ /* Compute the value of a Bernstein polynomial.*//* Input: i,n,u *//* Output: B */for (j=O; j<=n; j++) /* compute the columns */temp[j] = 0.0;/* of Table 1.1 */temp[n-i] = 1.0;/* in a temporary array */u1 = 1.0-u;for (k=1; k<=n; k++)for (j=n; j>=k; j--)temp[j] = u1*temp[j] + u*temp[j-1];B = temp[n];}