| OCR Text |
Show 70 the first derivative of a component described by Bezier [30], but defined cannot be 3. In the and loops. of The the of the not some techniques second derivative for each component of the normal the These a spline curve under tension be can defined,· it will be free of extraneous inflection bumps and loops caused by the interpolant avoided in the computation of the 4. by using existing information. where case that guaranteed bumps from a be obtained can interpolation is be cannot points, causing curve must be shading. done for each component of the normal. As the length normal at the vertices is of unit length, it is desirable that the length normal vector also is of unit interpolated obtained with any length. interpolation scheme, then a However, since this renormalization is of the normal would be necessary. 5. A time Every curve is under tension cannot .flt spline an required. set of a additional point is added, This nonlocal property a new given knots segment by segment, computation of the entire of the spline under tension spline causes many implementation problems. The a same difficulties encountered with a spline under tension arise when cubic function is used to interpolate the normal for shading. A cubic polynomial is defined as: ( 4.12) The linear coefficients equations. and yare necessary. In a, b, c, and d, are order to solve this the solutions of system of a system of equations, tour values four of x : |
