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Lecture 7

Lecture 7. Geometrical Transformations: 2D transformations 3D transformations Matrix representation OpenGL functions. Rendering Pipeline. Rendering Pipeline. Rendering Pipeline. Rendering Pipeline. Basic 2D Transformations. Basic 2D Transformations. Basic 2D Transformations.

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Lecture 7

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  1. Lecture 7 Geometrical Transformations: 2D transformations 3D transformations Matrix representation OpenGL functions

  2. Rendering Pipeline

  3. Rendering Pipeline

  4. Rendering Pipeline

  5. Rendering Pipeline

  6. Basic 2D Transformations

  7. Basic 2D Transformations

  8. Basic 2D Transformations

  9. Matrix representation

  10. Combination of 2D transformations

  11. 2x2 matrices

  12. 2x2 matrices

  13. 2x2 matrices

  14. 2x2 matrices

  15. 2x2 matrices • Only rotation, scaling, and shear can be represented in 2x2 matrix form. • These are linear transformations.

  16. Linear transformations

  17. 2D Translation: 3x3 matrix

  18. Homogeneous coordinates

  19. Basic 2D transformations in homogeneous coordinates

  20. Affine transformations

  21. Projections

  22. Matrix compositions

  23. Matrix compositions

  24. Matrix compositions

  25. 3D transformations

  26. Basic 3D transformations

  27. Basic 3D transformations

  28. OpenGL Matrix Stacks OpenGL works with stacks of 4x4 matrices: glMatrixMode(enum mode); mode: GL_MODELVIEWGL_PROJECTIONGL_TEXTURE Specifies whether the modelview, projection or texture matrix will be modified.

  29. OpenGL Matrix Stacks glLoadIdentity(void); Clears the currently modifiable matrix for future transformation instructions. Typically we call this instruction before specifying modeling, viewing or projection transformations.

  30. OpenGL Matrix Stacks Manipulating stacks: the OpenGL calls to push, pop, or multiply top of stack glLoadMatrix(void); glMultMatrix(void); glPushMatrix(void); the topmost matrix is copied glPopMatrix(void); the topmost matrix is destroyed All vertices of the object are multiplied by the matrix.

  31. OpenGL Matrix Stacks Manipulating stacks: the OpenGL calls to push, pop, or multiply top of stack glLoadMatrix(const type *m); glMultMatrix(const type *m); m1 m5 m9 m13 m2 m6 m10 m14 m3 m7 m11 m15 m4 m8 m12 m16

  32. OpenGL Matrix Stacks Manipulating stacks: the OpenGL calls to push, pop, or multiply top of stack glPushMatrix(void); the topmost matrix is copied glPopMatrix(void); the topmost matrix is destroyed All vertices of the object are multiplied by the matrix.

  33. OpenGL Transformations glTranslate(TYPE x, TYPE y, TYPE z); Multiplies the current matrix by a translation matrix. glRotate(TYPE angle, TYPE x, TYPE y, TYPE z); Multiplies the current matrix by a rotation matrix. glScale(TYPE x, TYPE y, TYPE z); Multiplies the current matrix by a scaling matrix.

  34. Summary • Types of transformations: • linear • affine • projective • Representation of transformations: • 3x3 and 4x4 matrices • homogeneous coordinates • Compositions of transformations • OpenGL Matrix Instructions

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