Graphics Pipeline: First Pass

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Graphics Pipeline First Pass
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Graphics Pipeline First pass

• Object representation (triangles) and computation
  of vertex attributes
  
• Model-view transformation
• Projection transformation
• Clipping and vertex interpolation of attributes
• Rasterization and pixel interpolation of
  attributes

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Object Representation

• Most common TRIANGLES
• Advantages
• Consistently planar
• Rotationally-invariant interpolation during
  rasterization
  
• Easy definition of topology as well as geometry
• Easy hardware implementation

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Object Representation

• Other representations
• Points (no connectivity information)
• Quadrilaterals (non-planarity, inconsistent
  interpolation of attributes)
  
• Images (no geometry not useful in simulations)
• Splines (to be converted to polygons for
  rasterization)

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Attributes

• Color (Red, Green, Blue)
• Normal vector
• Texture coordinate
• Transparency value
• .
• .
• .

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Graphics Pipeline First pass

• Object representation (triangles) and computation
  of vertex attributes
  
• Model-view transformation
• Projection transformation
• Clipping and vertex interpolation of attributes
• Rasterization and pixel interpolation of
  attributes

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Model-view transformations

• Model transformation
• View transformation

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Model transformations

• Transform the object to the required position,
  size and orientation.
  
• Can use any transformation to achieve this.
• In graphics library/hardware only linear
  transformations like rotate, translate, scale,
  shear are supported.

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View transformation

• Viewing parameters (9 parameters)
• View POINT (x,y,z),
• Viewing direction (VECTOR) (vx,vy,vz),
• View-up VECTOR (ux,uy,uz).
• Default (0,0,0), (0,0,-1), (0,1,0)
• Transforming the scene such that the view point
  is at the origin, viewing direction is aligned
  with the negative Z axis, and the view-up vector
  is aligned with the positive Y axis.
• Uses rotation and translation to achieve this
  transformation.

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Graphics Pipeline First pass

• Object representation (triangles) and computation
  of vertex attributes
  
• Model-view transformation
• Projection transformation
• Clipping and vertex interpolation of attributes
• Rasterization and pixel interpolation of
  attributes

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Projection Transformation

• Define the view frustum (6 parameters)
• Assume origin is the view point
• Near and far planes (planes parallel to XY plane
  in the negative Z axis)
  
• Left, right, top, bottom rectangle defined on the
  near plane.

-Z
Y
X
near
far
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Projection Transformation

• Transforming the view frustum (along with the
  objects inside it) into a cuboid with unit square
  faces on the near and far planes and with the
  negative Z axis passing through the center of
  these two faces.
• Consists of a shear and a perspective
  projection operations.

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Graphics Pipeline First pass

• Object representation (triangles) and computation
  of vertex attributes
  
• Model-view transformation
• Projection transformation
• Clipping and vertex interpolation of attributes
• Rasterization and pixel interpolation of
  attributes

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Clipping and Interpolation of Attributes

• Clipping Removing the portions of the polygon
  that is outside the view frustum. If the polygon
  spans inside and outside the view frustum,
  introduce new vertices on the boundary to remove
  the outside portion of the polygon.
• Interpolation For the new vertices introduced,
  compute all the attributes of the original
  vertices by interpolation.

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Window coordinate transformation

• After clipping, scale the square faces of the
  unit cuboid (square faced on the near and far
  planes) such that it represents the (relative)
  pixel coordinates. (You dont consider the Z
  value).
• Then translate these coordinates to the position
  of the window on the monitor screen to represent
  the absolute pixel coordinates.
  
• This is called window coordinate transformation.

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Graphics Pipeline First pass

• Object representation (triangles) and computation
  of vertex attributes
  
• Model-view transformation
• Projection transformation
• Clipping and vertex interpolation of attributes
• Rasterization and pixel interpolation of
  attributes

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Rasterization and Pixel Attribute Interpolation

• Rasterization is a process of generating pixels
  in the scan (horizontal) line order (top to
  bottom, left to right). (Also called scan
  conversion.)
• While generating pixels, the colors and other
  relevant attributes of the pixels are found by
  interpolating the attributes of the left and
  right extent of the scan line that lie on the
  polygon edge.

Scan Line
right
left
right
left
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Graphics Pipeline First pass

• End.