The Camera

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• Chapter 14
• The Camera

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This Chapter we will learn about

• Requirements of a Computer Graphics Camera
• Visible Volumes
• Perspective vs Orthorgraphics
• Coordinate Systems
• Eye (Camera) Coordinate System
• 3D Normalized Device Coordinate System
• 3D to 2D Perspective Projection

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A Computer Graphics Camera

• Camera position
• Look at position
• Up direction
• Related terms
• Image Plane
• Viewing Direction
• View Vector

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The Up Direction (Up Vector)

• Also referred to as Twist Angle
• Cannot be parallel to viewing direction
• Does not need to be normalized
• Does not need to be perpendicular toviewing
  direction

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Tut 14.1 Viewing Parameters

• All viewing parameterscontrolled by slider bars

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Tut 14.1 Controlling the Up Vector

• zslider
• Twist angle
• not perpendicularto View Vector!

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The Visible Volume

• Only geometries (primitives) inside the volume
  are visible
• All geometries (primitives) outside are ignored
• Primitives straddle the volume are Clipped!

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The Rectangular Visible Volume

• Volume defined by
• Near Plane (n)
• Far Plane (f)
• Width (W)
• Height (H)
• For Orthographic Projection

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Tut 14.2 Rectangular Visible Volume

• Experiment withRectangularVisibleVolume

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Tut 14.2 Orthographic Projection
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The Viewing Frustum Volume

• Volume defined by
• Near Plane (n)
• Far Plane (f)
• Fields of view (fov)
• For Orthographic Projection

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Near Plane and Aspect Ratio

• Aspect Ratio
• Near Plane
• Height (nh)
• Width (nw)

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Tut 14.3 Viewing Frustum

• Experiment withViewing Frustum

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Tut 14.3 Perspective Projection
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Orthographic vs Perspective Projection

• Orthographic Projection
• Parallel projection
• Preserve size
• Good for determining relative size
• Perspective Projection
• Projection along rays
• Closer objects appears larger
• Human vision!
• Only work with Perspective Projection

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Near-to-Far Plane distance

• Fixed number of bits to resolve distance
• E.g. 16-bits Unique positions
• If (f-n)18
• resolve distances larger than
• If (f-n) 106
• resolve distance larger than
• Rule of Thumb
• Minimize f and maximize n
• f-n As tight as possible

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Tut 14.4 Near/Far Distance

• Two squares very closeto each other
• Set n/f values to see errors!!

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Coordinate Transformation Pipeline

• Recall
• Transforms
• World Transform (MW)
• Object Space (OC) To World Space (WC)
• View Transform (MV)
• WC to Eye (Camera) Space (EC)
• Projection Transform (MP)
• EC To NDC (Normalize Device)

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The MW World Transform

• Transformation
• From Object Space to World Space
• Identical to 2D!
• Refer to discussions
• In Chapter 11 World Coordinate System
• Library Implementation
• SceneNodes Transform operator!
• DrawHelper Matrix Stack Manipulations!

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The MV View Transform

• Transformation
• From World to Eye Space
• Referred to as
• Eye, or View, or Camera Transform
• Topics
• Eye Coordinate Orthonormal Basis
• The Eye Coordinate (EC) Space
• Aligning EC and WC Orthonormal Basis
• The WC to EC Transform

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The EC Orthonormal Basis

• Viewing Parameters Eye Position At
  Position Up Vector
• View Vector
• Side Vector
• Adjusted Up Vector

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Example
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The Eye Coordinate Space

• Origin eye position
• Axes Directions
• View -z
• Up y
• Side x
• Visible Volume
• Near z-n
• Far z-f

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Align EC and WC Orthonormal Basis
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MV Mw2e WC To EC Transform
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Inverse Transform Me2w

• Row-4 is The Eye Position!!

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The MP Projection Transform

• Transform from EC to NDC
• Recall NDC Range
• Transform
• Squeeze the View Frustum into NDC Cube

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View Frustum to NDC Cube
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3D NDC to 2D Image (Near) Plane
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Re-Examine Tutorial 13.1

• GrfxWindowOnPaint()