Đang chuẩn bị liên kết để tải về tài liệu:
computer graphics c version phần 9

như một mở rộng Taylor-series và giữ lại các điều khoản lên đến mức độ thứ hai trong x và y. Điều này mang lạiT từng là một chức năng của các thông số a, b, c, và vv. Sử dụng sự khác biệt về phía trước, chúng ta có thể đánh giá Eq. 14-48 với chỉ có hai bổ sung cho pixel từng vị trí (x, y) | Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com We can rewrite this expression in the form Section 14-6 Ray-Tracin g Methods ax by c eXy ỷyĩ gx hy i l 2 14 46 where parameters sụch as a b c and d are used to represent the various dot products. For example L A a IIJ 7 Finally we can express the denominator in Eq. 14-46 as a Taylor-series expansion and retain terms up to second degree in X and y. This yields w . y T-J1 Tpry ry2 T2X T y To i4-4 where each Tk is a function of parameters a b c and so forth. Using forward differences we can evaluate Eq. 14-48 with only two additions for each pixel position x ỳ once the initial forward-difference parameters have been evaluated. Although fast Phong shading reduces the Phong-shading calculations it still takes approximately twice as long to render a surface with fast Phong shading as it does with Gouraud shading. Normal Phong shading using forward differences takes about six to seven times longer than Gouraud shading. Fast Phong shading for diffuse reflection can be extended to include specular reflections. Calculations similar to those for diffuse reflections are used to evaluate specular terms such as N H ns in the basic illumination model. In addition we can generalize the algorithm to include polygons other than triangles and finite viewing positions. 14-6__ RAY-TRACING METHODS In Section 10-15 we introduced the notion of ray casting where a ray is sent out from each pixel position to locate surface intersections for object modeling using constructive solid geometry methods. We also discussed the use of ray casting as a method for determining visible surfaces in a scene Section 13-10 . Ray tracing is an extension of this basic iộea. Instead of merely looking for the visible surface for each pixel we continue to bounce the ray around the scene as illustrated in Fig. 14-49 collecting intensity contributions. This provides a .