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computer graphics c version phần 4

là không có nút giao thông tự. Ví dụ đa giác tiêu chuẩn bao gồm các hình tam giác, hình chữ nhật, octagons, và decagons. Các cạnh thành phần của các đối tượng này được tham gia chỉ ở các đỉnh, và nếu không các cạnh không có điểm chung trong máy bay. | Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com Chapter 5 Two-Dimensional Geometric Transformations Scalings Concatenating transformation matrices for two successive scaling operations produces the following composite scaling matrix 0 syl sy2 0 o 0 1 5-29 or S Sj2 Syj S rJ Syị S Syl sx2 Sy I Syj 5-30 The resulting matrix in this case indicates that successive scaling operations are multiplicative. That is tf we were to triple the size of an object twice in succession the final size would be nine times that of the original. General Pivot-Point Rotation With a graphics package that only provides a rotate function for revolving objects about the coordinate origin we can generate rotations about any selected pivot point xr yr by performing the following sequence of translate-rotate-translate operations 1. Translate the object so that the pivot-point position is moved to the coordinate origin. 2. Rotate the object about the coordinate origin. 3. Translate the object so that the pivot point is returned to its original position. This transformation sequence is illustrated in Fig. 5-9. The composite transforma- Ptvot Point Origin orObfactand Pivot Point r ransAH on or Object o that the Pivot Point Is Returned to Position Figure 5-9 A transformation sequence for rotating an object about a specified pivot point using the rotation matrix R S of transformation 5-19. 192 Simpo PDF Merge and Split Unregistered Version - http www.simpopdf.com tion matrix for this sequence IS obtained with the concatenation Section 5-3 . . Composite Transformations 1 u X cos Ỡ -sin 0 0 10 - X 0 1 yr sin 0 cos 0 0 0 1 -y 0 0 1 0 0 1 0 0 1 cos 6 -sin ị 1 1 - cos 9 4- y sin Ỡ sin 6 cos Ỡ y l - cos 9 - X sin Ỡ 5 31 0 0 1 which can be expressed in the form T x y R ớ - TÍ-X -yf - R x y 0 .5-321 where T -x - y. T ỵ xr yr . In general a rotate function can be set up to accept parameters for pivot-point coordinates as well as the rotation angle and to generate automatically the .