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Three-Dimensional Viewing Clipping

Three-Dimensional Viewing Clipping. Computer Graphics C Version (456p - 462p). Objectives of this Chapter. General Ideas How clipping could be performed using the view volume Normalized view volume Homogeneous coordinates . General Ideas for 3D Clipping. A Point of Similarity

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Three-Dimensional Viewing Clipping

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  1. Three-Dimensional ViewingClipping Computer Graphics C Version (456p - 462p)

  2. Objectives of this Chapter • General Ideas • How clipping could be performed using the view volume • Normalized view volume • Homogeneous coordinates

  3. General Ideas for 3D Clipping • A Point of Similarity • Accomplished with extensions of 2D clipping method • A Point of Difference • Clipping against boundary planes of view volume instead of boundary edge

  4. Line Clipping - 1 • View volume’s boundary plane Eq • Ax + By + Cz + d = 0 • If point is (x, y, z) • Inside boundary: Ax + By + Cz + d < 0 • Outside boundary: Ax + By + Cz + d > 0

  5. Line Clipping - 2 • Cases of 2 end points’ position • All inside • Saved • All outside • Discard • Leaving intersection • One inside, one outside • Leaving intersection • Intersection coordinate (xi, yi, zi) Axi + Byi + Czi + d = 0

  6. Viewing Transformation - 1 • Expanded PHIGS transformation pipeline

  7. Viewing Transformation - 1 • View Volume Clipping • Rectangular parallelepiped view volume Clipping • Unit cube clipping

  8. Viewing Transformation - 1

  9. Viewing Transformation - 2 • View Volume Clipping • Needs to obtain all 6 planes equations • Rectangular parallelepiped view volume Clipping • Each surface is perpendicular to one coordinate axes • Converting to Rect parallelepiped view volume Orthographic view volume Oblique view volume Perspective view volume

  10. Viewing Transformation - 3 • Unit cube clipping • Providing standard shape for representing any sized view volume • Providing simplified clipping procedure • Providing simplified depth cueing and visible-surface determination ->Normalized view volume

  11. Normalized View Volume • Dimensions of the view volume and 3D viewport

  12. Normalized View Volume Dx= Dz= Dy= Kx= Ky= Kz=

  13. Viewport Clipping • Cohen Sutherland (6 Bit code) • Bit 1 =1 x<XVmin (left) • Bit 2 =1 x<XVmax (right) • Bit 3 =1 y<YVmin (below) • Bit 4 =1 y>YVmin (above) • Bit 5 =1 z<ZVmin (front) • Bit 6 =1 z>ZVmax (back) • Cyrus-Beck or Liang-Barsky • X = X1 + (X2 - X1)u • Y = Y2 + (Y2 - Y1)u • Z = Z3 + (Z2 – Z1)u

  14. Clipping in Homogeneous Coordinates • Conversion • (x, y, z) -> (x, y, z, 1) X’= Y’= Z’= =

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