1 / 31

Chapter 4

Chapter 4. 15 March 2006. EventPro Strategies is looking for a part-time programmer (any language) who knows SQL. For more info, contact Ryan Taylor, ryan@eventprostrategies.com. Agenda. Chapter 4 – Math for Computer Graphics GLUT solids. Transformations.

kaori
Download Presentation

Chapter 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 4 15 March 2006 EventPro Strategies is looking for a part-time programmer (any language) who knows SQL. For more info, contact Ryan Taylor, ryan@eventprostrategies.com

  2. Agenda • Chapter 4 – Math for Computer Graphics • GLUT solids

  3. Transformations • 45-degree counterclockwise rotation about the origin around the z-axis • a translation down the x-axis

  4. Order of transformations glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glMultMatrixf(N); /* apply transformation N */ glMultMatrixf(M); /* apply transformation M */ glMultMatrixf(L); /* apply transformation L */ glBegin(GL_POINTS); glVertex3f(v); /* draw transformed vertex v */ glEnd(); • transformed vertex is NMLv

  5. Translation • void glTranslate{fd} (TYPE x, TYPE y, TYPE z); • Multiplies the current matrix by a matrix that moves (translates) an object by the given x, y, and z values

  6. Rotation • void glRotate{fd}(TYPE angle, TYPE x, TYPE y, TYPE z); • Multiplies the current matrix by a matrix that rotates an object in a counterclockwise direction about the ray from the origin through the point (x, y, z). The angle parameter specifies the angle of rotation in degrees.

  7. Scale • void glScale{fd} (TYPEx, TYPE y, TYPEz); • Multiplies the current matrix by a matrix that stretches, shrinks, or reflects an object along the axes.

  8. Vectors • N tuple of real numbers (n = 2 for 2D, n = 3 for 3D) • directed line segment • example • velocity vector (speed and direction) • operations • addition • multiplication by a scalar • dot product

  9. VectorsVector and Vector Algebra 1 2 3 2 + 3 = 5 3 4 7

  10. Matrices • Rectangular array of numbers • Addition • QuickMath

  11. 1 3 1 Matrices • A vector in 3 space is a n x 1 matrix or column vector.

  12. Matrices • Multiplication 1 0 0 0 0 1 0 0 x 0 0 0 0 0 0 1/k 1 Cos α 0 sin α 0 0 1 0 m -sin α 0 cos α n 0 0 0 1

  13. Matrix multiplication • A is an n x m matrix with entries aij • B is an m x p matrix with entries bij • AB is an n x p matrix with entries cij m • cij = ais bsj s=1

  14. Matrix multiplication m • cij = ais bsj s=1 c11c12 c13 c14 c21c22 c23 c24 c31c32 c33 c34 c41c42 c43 c44 1 0 0 0 0 1 0 0 x 0 0 0 0 0 0 1/k 1 Cos α 0 sin α 0 0 1 0 m -sin α 0 cos α n 0 0 0 1 a b

  15. 2D Transformations • Translation: Pf = T + P xf = xo + dx yf = yo + dy • Rotation: Pf = R · P xf = xo * cos - yo *sin yf = xo * sin + yo *cos • Scale: Pf = S · P xf = sx * xo yf = sy * yo

  16. Homogeneous Coordinates • Want to treat all transforms in a consistent way so they can be combined easily • Developed in geometry (‘46 in Cambridge) and applied to graphics • Add a third coordinate to a point (x, y, W) • (x1, y1, W1) is the same point as (x2, y2, W2) if one is a multiple of another • Homogenize a point by dividing by W

  17. Homogeneous Coordinates 1 0 dx x 0 1 dy · y 0 0 1 1

  18. Homogeneous Coordinates sx 0 0 x 0 sy 0 · y 0 0 1 1

  19. Homogeneous Coordinates Cos -sin0 x sin cos0 · y 0 0 1 1

  20. Combining 2D Transformations • Rotate a house about the origin • Rotate the house about one of its corners • Translate so that a corner of the house is at the origin • Rotate the house about the origin • Translate so that the corner returns to its original position

  21. GLUT Solids • Sphere • Cube • Cone • Torus • Dodecahedron • Octahedron • Tetrahedron • Icosahedron • Teapot

  22. glutSolidSphere and glutWireSphere • void glutSolidSphere(GLdouble radius, GLint slices, GLint stacks); • radius - The radius of the sphere. • slices - The number of subdivisions around the Z axis (similar to lines of longitude). • stacks - The number of subdivisions along the Z axis (similar to lines of latitude).

  23. glutSolidCube and glutWireCube • void glutSolidCube(GLdouble size); • size – length of sides

  24. glutSolidCone and glutWireCone • void glutSolidCone(GLdouble base, GLdouble height, GLint slices, GLint stacks); • base - The radius of the base of the cone. • height - The height of the cone. • slices - The number of subdivisions around the Z axis. • stacks - The number of subdivisions along the Z axis.

  25. glutSolidTorus and glutWireTorus • void glutSolidTorus(GLdouble innerRadius,GLdouble outerRadius, GLint nsides, GLint rings); • innerRadius - Inner radius of the torus. • outerRadius - Outer radius of the torus. • nsides - Number of sides for each radial section. • rings - Number of radial divisions for the torus.

  26. glutSolidDodecahedron and glutWireDodecahedron • void glutSolidDodecahedron(void);

  27. glutSolidOctahedron and glutWireOctahedron . • void glutSolidOctahedron(void);

  28. glutSolidTetrahedron and glutWireTetrahedron • void glutSolidTetrahedron(void);

  29. glutSolidIcosahedron and glutWireIcosahedron • void glutSolidIcosahedron(void);

  30. glutSolidTeapot and glutWireTeapot • void glutSolidTeapot(GLdouble size); • size - Relative size of the teapot.

  31. Homework next week. • Study for Test on Chapters 1-4, 02/15/05

More Related