[图形学]3D数学基础_图形与游戏开发(习题答案).doc

Answers Chapter 2 Give the coordinates of the following points: a (-2.5, 3) b (1, 2) c (2.5, 2) d (-1, 1) e (0, 0) f (2, -0.5) g (-0.5, -1.5) h (0, -2) j (-3, -2) 1  List the 48 different possible ways that the 3D axes may be assigned to the directions “north,” “east” and “up.” Identify which of these combinations are left-handed, and which are right-handed. North East Up Hand North East Up Hand +x +y +z Left +x +z +y Right +x +y –z Right +x +z –y Left +x –y +z Right +x –z +y Left +x –y –z Left +x –z –y Right –x +y +z Right –x +z +y Left –x +y –z Left –x +z –y Right –x –y +z Left –x –z +y Right –x –y –z Right –x –z –y Left +y +x +z Right +y +z +x Left +y +x –z Left +y +z –x Right +y –x +z Left +y –z +x Right +y –x –z Right +y –z –x Left –y +x +z Left –y +z +x Right –y +x –z Right –y +z –x Left –y –x +z Right –y –z +x Left –y –x –z Left –y –z –x Right +z +x +y Left +z +y +x Right +z +x –y Right +z +y –x Left +z –x +y Right +z –y +x Left +z –x –y Left +z –y –x Right –z +x +y Right –z +y +x Left –z +x –y Left –z +y –x Right –z –x +y Left –z –y +x Right –z –x –y Right –z –y –x Left In a popular modeling program 3D Studio Max, the default orientation of the axes is for +x to point right, +y to point forward, and +z to point up. Is this a left- or right-handed coordinate space? Right-handed. 2  Chapter 3  Draw a nested space hierarchy tree for the sheep described in Section 3.3, assuming that its head, ears, upper legs, lower legs, and body move indemendently. Suppose our object axes are transformed to world axes by rotating them counterclockwise around the y-axis by 42o and then translating six units along the z-axis and 12 units along the x-axis. Describe this transformation from the perspective of the object. Imagine a point on the object, in object space. As the axes are rotating counterclockwise, the point is actually rotating counterclockwise r