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3D Graphics Introduction Part 1

3D Graphics Introduction Part 1. CIS 488/588 Bruce R. Maxim UM-Dearborn. 3D Game Engine - 1. 3D Engine Software that processes the 3D world data structures and renders them from camera’s viewpoint (it does not do physics processing) Game Engine

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3D Graphics Introduction Part 1

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  1. 3D Graphics IntroductionPart 1 CIS 488/588 Bruce R. Maxim UM-Dearborn

  2. 3D Game Engine - 1 • 3D Engine • Software that processes the 3D world data structures and renders them from camera’s viewpoint (it does not do physics processing) • Game Engine • Controlling module that sends commands to all subsystems (calls the 3D Engine - not part of it)

  3. 3D Game Engine - 3 • Input System and Networking • Keep game separate from networking module (not part of 3D engine, AI, or physics) • Network support for 3D games must be designed early in the development cycle • Animation System • Simple Motion • Complex Animation • Physically-based Animation

  4. Simple Motion • Basic translation and rotation of game objects • Might be tied to AI if objects need to move as units and physics to determine if movement is possible or not • Where to put the knowledge depends on the complexity of the game itself

  5. Complex Animation • Implies the existence of articulated-hierarchical objects with links that must move in relation to each other (e.g. robot tank with an upper body moving turret) • Could be done by blitting frames from meshes • Can be done with motion data (e.g. BioVision) - similar to midi philosophy, link movement are scripted in relation to each other for independent playback – problem is where to place check for feedback

  6. Physically-Based Animation • The laws of physics control all movement • For example fighting moves are pre-recorded motion capture data which is fed into the physically-based animation system that controls the physics models that perform the animation • The physically-based animation, animation, and physics systems are intimately connected (but not the 3D engine that only renders the polygon list without knowing how it was created)

  7. 3D Game Engine - 4 • Collision Detection and Navigation • May be the only physics system needed for simple game (feedbacks to AI and animation systems) • Physics Engine • Friction forces and acceleration • Elastic collision detection and response • Linear momentum transfer • Has nothing to do with 3D visual representation (though it does need to be tied in to the AI and animation systems)

  8. 3D Game Engine - 5 • AI System • All AI algorithms become harder to implement in 3D than in 2D • Usually tied to the animation and physics systems • 3D Model and Imagery Database • 3D meshes for objects • 2D texture maps and light maps • Motion and animation data • Game map data

  9. 3D Viewing Pipeline • Model (local) coordinates • World coordinates • Camera coordinates • Perspective coordinates • Screen coordinates

  10. Model (local) Coordinates • Coordinates assuming the center of object is centered at (0,0,0) or some other point • Convention might call for “front” pointing in z+ axis direction and “top” pointing in y+ axis direction • Alternatively the longest object axis can be aligned with z+ and the second longest object axis can be aligned with y+ • Model all objects using the same scale and adjust the scale during rendering if needed

  11. World Coordinates • Actual coordinates in virtual world • Need to keep unit in mind (affects storage and speed of traversal at 30 fps) • To translate from model coordinates to world coordinates is done by translating the object | 1 0 0 0 | Twm = | 0 1 0 0 | | 0 0 1 0 | | x y z 1 |

  12. Camera Coordinates • Camera coordinates • In 3D games the camera moves around • The camera is placed at (cam_x, cam_y, cam_z) pointed in direction (pitch,yaw,roll) • Field of view parameters define define what can be seen in the horizontal and vertical directions • To simulate human vision 110-120 degrees horizontally and < 90 degrees vertically • The 3D viewing frustrum is used to describe these relationships

  13. Viewing Frustrum • Objects closer than the near_z clipping plane or farther than the far_z clipping plane are not rendered • The side planes are also used to clip the object that are to be rendered, with a 90% viewing volume each side plane is 45% to the view direction with equations |x|=z and |y|=z • To pretend the camera is at (0,0,0) and looking down the z+ axis requires a transformation (translate then rotate)

  14. World to Camera - 1 • Translation step using Tcam-1 | 1 0 0 0 | [xw yw zw 1] * | 0 1 0 0 | = | 0 0 1 0 | | -cam_x –cam_y –cam_z 1 | = [xw-cam_x yw-cam_yzw-camz 1 ]

  15. World to Camera - 2 • Rotation Rcamx-1 | 1 0 0 0 | | 0 cos(-ang_x) sin(-ang_x) 0 | | 0 –sin(-ang_x) cos(-ang_x) 0 | | 0 0 0 1 | • Rotation Rcamy-1 |cos(-ang_y) 0 -sin(-ang_y) 0 | | 0 1 0 0 | |sin(-ang_y) 0 cos(-ang_y) 0 | | 0 0 0 1 |

  16. World to Camera - 2 • Rotation Rcamz-1 | cos(-ang_z) sin(-ang_z) 0 0 | |-sin(-ang_z) cos(-ang_z) 0 0 | | 0 0 1 0 | | 0 0 0 1 | • The complete transformation is Twc = Tcam-1 * Rcamy-1 *Rcamx-1 *Rcamz-1

  17. Gimbal Lock • Occurs when one axis is rotated to the point that it becomes aligned with another and further rotation results in no movement at all • For example if the x-axis is rotated 90 degrees it could align with the y-axis so that rotating around the x-axis has no effect

  18. Hidden Surface Removal • How do you know which objects are visible to camera before you so they are not transformed or rendered? • Commonly used techniques • Back-face removal • Bounding spheres test

  19. Back-Face Removal - 1 • Step 1: • Remove all polygons outside of viewing frustum • Step 2: • If the dot product of the view vector and the surface normal is > 0, it is facing the viewer. • Remove all polygons that are facing away from the viewer.

  20. Back-Face Removal - 2 • Step 3: • Draw the visible faces in an order so the object looks right. • Note: • Surface normal = cross product of two co-planar edges. • View vector from normal point to viewpoint

  21. Bounding Sphere Test –1 • Can be used before back-face removal to discard entire objects all at once • This test only works if you have object partitioned in convex areas, won’t work for a game world composed of a single mesh • The idea is to create a bounding sphere around each object and then transform Twc the center of each sphere and see if the entire sphere is outside the viewing frustrum

  22. Bounding Sphere Test – 2 • If none of the points p1-p5 is in the viewing frustrum the object can not be visible, the general test for point p(x,y,z) is outside if ((z > far_z) || (z < near_z) || // z-axis (fabs(x) < z)|| //x-z plane (fabs(y) < z)) //y-z plane { // point not in viewing frustrum }

  23. Bounding Sphere Test – 3 • It is important to note that just because a portion of the bounding sphere is inside the viewing frustrum there is no guarantee that any portion of the object is visible (unless the object is a sphere that fill the entire bounding sphere exactly) • Might be better to use a bounding cube or parallelepiped depending on the shape of the object

  24. Projection Overview - 1 • Once the object has been transformed and it lies in the viewing frustrum we have to decide how to project the image onto screen • Selecting the location of the viewing plane inside the viewing frustrum can make things either easier or harder farther down the viewing plane

  25. Projection Overview - 2 Perspective projection View Plane Parallel projection

  26. Projection Overview - 3 • Parallel • If viewing down z-axis, just discard z component • Perspective • If viewing down z-axis, scale points based on distance. • x_screen = x / z • y_screen = y / z

  27. Projection Overview - 4 • Usually not viewing down center of z axis. • Usually x = 0 and y = 0 at bottom left • Correct by adding 1/2 screen size • x_screen = x/z + 1/2 screen width • y_screen = y/z + 1/2 screen height • To get perspective right, need to know field of view, distance to screen, aspect ratio. • Often add scaling factor to get it to look right • x_screen = x*scale /z + 1/2 screen width

  28. Perspective Transformation - 1 • Equations xper = d * x / z yper = d * y / z • Matrix Transformation Tper | 1 0 0 0 | [xc yc zc 1] * | 0 1 0 0 | = | 0 0 1 1/d | | 0 0 0 0 | = [xc yc zc (zc/d)]

  29. Perspective Transformation - 2 • The viewing distance can be anything so consider using d= 1 to end up with normalized view plane coordinates • Matrix Transformation Tper1 | 1 0 0 0 | [xc yc zc 1] * | 0 1 0 0 | | 0 0 1 1 | | 0 0 0 0 |

  30. Perspective Transformation - 3 • The viewing screen is not square you need to take the aspect ratio into account xper = d * x / z yper = d * y * ar / z d = (0.5) * width * tan(h / 2) • Matrix Transformation Tper1 | d 0 0 0 | [xc yc zc 1] * | 0 d*ar 0 0 | = | 0 0 1 1 | | 0 0 0 0 | = [(d*xc) (d*yc*ar)zc zc]

  31. Clipping - 1 • This affects objects that are neither completely inside nor completely outside the viewing frustrum • Image Space Line Clipping • Use perspective projection to put all line on the screen • Clip lines during the rasterization phase of the 3D pipeline (so every object is processed for clipping even if it is completely inside viewing frustrum)

  32. Clipping – 2 • Object Space Line Clipping • Use object space clipping to eliminate the objects that will not be visible before performing the perspective transformation • The idea is to use the perspective transformation to normalize the viewing frustrum by transforming it to a viewing cuboid that will make clipping perspective coordinates fairly easy

  33. Screen Coordinates • Lighting and texture issues are ignored for the time being • Computing screen coordinates will depend on the kind of perspective transformation that was used • The aspect ratio will need to be taken into account for non-square screens

  34. Screen Transformation - 1 • Equations d = 1 and FOV = 90 degrees xscreen = (xper + 1) * (0.5 * SCREEN_WIDTH - 0.5) yscreen = (SCREEN_HEIGHT – 1) – (yper+ 1) * (0.5 * SCREEN_HEIGHT - 0.5) • These equations can be simplified if  = (0.5 * SCREEN_WIDTH - 0.5)  = (0.5 * SCREEN_HEIGHT - 0.5) xscreen =  + xper *  yscreen =  - yper * 

  35. Screen Transformation - 2 • Matrix Transformation Tscr1 |  0 0 0 | [xper yper 0 1] * | 0 - 0 0 | = | 0 0 1 0 | |  0 1 | = [(xper* + ) (-yper* + )0 1 ]

  36. Screen Transformation - 3 • Equations for arbitary d and FOV xscreen = xper + (0.5 * SCREEN_WIDTH - 0.5) yscreen = -yper + (0.5 * SCREEN_HEIGHT - 0.5) • These equations can be simplified if  = (0.5 * SCREEN_WIDTH - 0.5)  = (0.5 * SCREEN_HEIGHT - 0.5) xscreen = xper +  yscreen = -yper + 

  37. Screen Transformation - 4 • Matrix Transformation Tscr | 1 0 0 0 | [xper yper 0 1] * | 0 -1 0 0 | = | 0 0 1 0 | |  0 1 | = [(xper + ) (-yper + ) 0 1 ]

  38. Screen Transformation - 5 • Equations for arbitary d and FOV xscreen = d*xcam/zcam + (0.5 * SCREEN_WIDTH - 0.5) yscreen = -d*ycam/zcam + (0.5 * SCREEN_HEIGHT - 0.5) • These equations can be simplified if  = (0.5 * SCREEN_WIDTH - 0.5) • = (0.5 * SCREEN_HEIGHT - 0.5) d = (0.5) * viewplane_width * tan(h) xscreen = d*xc/zc +  yscreen = -d*yc/zc + 

  39. Screen Transformation - 6 • Matrix Transformation Tcamscr | d 0 0 0 | [xc yc zc 1] * | 0 -d 0 0 | = |  1 1 | | 0 0 0 0 | = [(d*xc + zc*) (-d*yc + zc*) zc zc ]

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