AngelCG13图形学.ppt

Angel: Interactive Computer Graphics 4E ? Addison-Wesley 2005 OpenGL Transformations Shandong University Software College Instructor: Xu Yanning E-mail: xyn@sdu.edu.cn Objectives Learn how to carry out transformations in OpenGL Rotation Translation Scaling Introduce OpenGL matrix modes Model-view Projection OpenGL Matrices In OpenGL matrices are part of the state Multiple types Model-View (GL_MODELVIEW) Projection (GL_PROJECTION) Texture (GL_TEXTURE) (ignore for now) Color(GL_COLOR) (ignore for now) Single set of functions for manipulation Select which to manipulated by glMatrixMode(GL_MODELVIEW); glMatrixMode(GL_PROJECTION); Current Transformation Matrix (CTM) Conceptually there is a 4 x 4 homogeneous coordinate matrix, the current transformation matrix (CTM) that is part of the state and is applied to all vertices that pass down the pipeline The CTM is defined in the user program and loaded into a transformation unit CTM operations The CTM can be altered either by loading a new CTM or by postmutiplication Rotation about a Fixed Point Start with identity matrix: C ? I Move fixed point to origin: C ? CT Rotate: C ? CR Move fixed point back: C ? CT -1 Result: C = TR T –1 which is backwards. This result is a consequence of doing postmultiplications. Let’s try again. Reversing the Order We want C = T –1 R T so we must do the operations in the following order C ? I C ? CT -1 C ? CR C ? CT Each operation corresponds to one function call in the program. Note that the last operation specified is the first executed in the program CTM in OpenGL OpenGL has a model-view and a projection matrix in the pipeline which are concatenated together to form the CTM Can manipulate each by first setting the correct matrix mode Rotation, Translation, Scaling glRotatef(theta, vx, vy, vz) Example Rotation about z axis by 30 degrees with a fixed point of (1.0, 2.0, 3.0) Remember that last matrix specified in the program is the first applied Arbitrary Matrices Can load and