1 / 29

OpenGL (II)

OpenGL (II). How to Draw a 3-D object on Screen?. Drawing a Scene. Apply modeling and viewing transformations Apply projection transformation Clip if it lies outside the viewing volume Apply viewport transformation to display on the screen. Transformations.

fausto
Download Presentation

OpenGL (II)

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. OpenGL (II)

  2. How to Draw a 3-D object on Screen?

  3. Drawing a Scene • Apply modeling and viewing transformations • Apply projection transformation • Clip if it lies outside the viewing volume • Apply viewport transformation to display on the screen

  4. Transformations • Modeling Transformation • Viewing Transformation • Projection Transformation • Viewport Transformation

  5. Stages of Vertex Transformations • Object Local Coordinates • ModelView • Matrix • Projection • Matrix • Eye Coordinates • Vertex • Clip Coordinates • Normalized Device Coordinates • Viewport • Transformation • Perspective • Division • Windows Coordinates

  6. Transformations in OGL • Recall that once you define the attributes (such as color), all the subsequent objects are drawn using those attributes. • Same rule applied for transformations • Specify a transformation, and then this transformation is automatically applied to every object that is drawn, until the transformation is set again. • Important: set transformations prior to drawing

  7. Transformations in OGL • Transformations have different purposes • We discuss only two of OGL’s matrix types (the third is Texture matrix) • Modelview matrix for moving objects or change of coordinates • Projection matrix for projection • Project objects from the world window to the viewport, and mapping the viewport to the graphics display window.

  8. Transformations in OGL • For each matrix type, OGL maintains a stack of matrices • Stack: last in, first out • To operate on a specific matrix type,call glMatrixMode(mode) • Different modes: GL_MODELVIEW, GL_PROJECTION • Once the matrix mode is set, performvarious operations on the stack.

  9. Matrix Stacks (Con’t) • There are several routines for manipulating matrix stacks • glPushMatrix() • glPopMatrix() • glLoadMatrix() • glMultMatrix() • glLoadIdentity() • To avoid destroying the contents of the Modelview matrix, save the contents of the Modelview matrix and restore its contents after we are done.

  10. Modeling Transformation • Positions and orients the objects • Rotation: glRotate{fd}(angle, x, y, z) • Translation: glTranslate{fd}(x, y, z) • Scaling: glScale{fd}(x, y, z)

  11. Model space World space Model space Modeling Transformation (Con’t)

  12. Transformation Example • In OGL, whenever you draw, the points are automatically transformed using the current Modelview matrix. • Common way of object transformations in OGL • Push the matrix stack. • Apply all desired transformations • Draw your objects (the transformations will be applied automatically) • Pop the matrix stack.

  13. M M MT MTR M M M Post-multiplication glTranslate() glPushMatrix() glRotate()

  14. Order of Transformations • Specify the transformations in the reverse order of the way you conceptualize them Specify M1M2v Conceptualize

  15. Order of Transformations (Con’t) • Example 1: TRv glTranslatef(2.0,0.0,0.0) glRotatef(45.0,0.0,0.0,1.0)

  16. Order of Transformations (Con’t) • Example 2: RTv glRotatef(45.0,0.0,0.0,1.0) glTranslatef(2.0,0.0,0.0)

  17. Transformation Example • First attempt • Rotation command • glRotatef(angle_in_degree, x, y, z); • Rotation is performed about the origin of the coordinate system. • Translation command • glTranslatef(x, y, z); glPushMatrix(); // save the current matrix glRotatef(20, 0, 0, 1); // rotate by 20 degrees CCW glRectf(x-2, y-2, x+2, y+2); // draw the rectangle glPopMatrix(); // restore the old matrix equivalent glPushMatrix(); // save the current matrix glRotatef(20, 0, 0, 1); // rotate by 20 degrees CCW glTranslatef(x, y, 0); // apply translation glRectf(-2, -2, 2, 2); // draw the rectangle glPopMatrix(); // restore the old matrix

  18. Transformation Example • Correct way glPushMatrix(); // save the current matrix glTranslatef(x, y, 0); // apply translation glRotatef(20, 0, 0, 1); // rotate by 20 degrees CCW glRectf(-2, -2, 2, 2); // draw the rectangle glPopMatrix(); // restore the old matrix

  19. OpenGL viewing • Modelview transformation • Modeling transformation: local coordinates  world coordinates • Viewing transformation: world coordinates  eye coordinates

  20. Modelview Matrix • Pulling the camera back from the object (viewing transformation) moving the object away from the camera (modeling transformation) • Thus, both viewing and modelingtransformations are stored in the modelview matrix stack

  21. y x z Viewing Transformation • Position and aim the camera • gluLookAt(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz) • Default location at origin looking down the negative z-axis

  22. Viewing Transformation (Con’t) Up vector Eye position Center position

  23. OpenGL viewing • gluLookAt(eye.x, eye.y, eye.z, center.x, center.y, center.z, up.x, up.y, up.z) • Viewing direction: center – eye • Up is the upward direction • Viewing direction and up vector eye coordinate system • X axis points to the right of viewer • Y axis points upward • Z axis points to the back of viewer • Generate a matrix, which is postmultiplied to the top-of-the-stack matrix on the Modelview stack • Thus, must be called before any modeling transformations

  24. OpenGL viewing • Default OpenGL viewing (if no gluLookAt is specified) • Eye is at origin of world space • Looking down the negative z axis of world space • Up vector is positive y axis • The viewing transformation matrix is identity matrix (i.e. eye coordinate system = world coordinate system)

  25. Viewing Transformation (Con’t) gluLookAt(4.0, 2.0, 1.0, 2.0, 4.0, -3.0, 2.0, 2.0, -1.0) Default location

  26. OpenGL projection • glOrtho(), gluPerspective() or glFrustum() • Produce a matrix which is stored in the projection matrix stack • All geometry objects are already transformed to the eye coordinate system before projection transformation is applied • The parameters of these functions are with respect to the eye coordinate system • The parameters define 6 clipping planes • To simplify clipping, the viewing space is transformed into a canonical view volume (all coordinates in [-1, +1])

  27. OpenGL orthographic projection glOrtho(left, right, bottom, top, near, far) • left, right, bottom, top are coordinates in eye space • left, right are the x-coordinate limits • bottom, top are the y-coordinate limits • near, far are signed distances from the eye to the near and far clipping planes (e.g., near = 2, far = 15 mean the clipping planes are at z=-2 and z= -15)

  28. OpenGL perspective projection • The center of projection and the portion of the projection plane that map to the final image form an infinite pyramid. The sides of the pyramid are clipping planes. • All of the clipping planes bound the viewing frustum. • In OpenGL, PP = near plane

  29. OpenGL perspective projection glFrustum(left, right, bottom, top, near, far) • View frustum may not be centered along view vector • Less often used than gluPerspective() gluPerspective(fov_y, aspect_ratio, near, far) • fov_y is vertical field-of-view in degrees • aspect ratio = width / height • near, far are distances from eye to two clipping planes • must be positive • Keep them close so as to maximize depth precision

More Related