Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Chapter 14: The Camera
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
A Computer Graphics Camera
Camera position Look at position Up direction Related terms:
Image Plane Viewing Direction View Vector
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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 to
viewing direction
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Tut 14.1: Viewing Parameters
All viewing parameterscontrolled by slider bars
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
z=slider:
Twist angle:
not perpendicularto View Vector!
Tut 14.1: Controlling the Up Vector
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
The Visible Volume
Only geometries (primitives) inside the volume are visible
All geometries (primitives) outside are ignored
Primitives straddle the volume are Clipped!
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
The Rectangular Visible Volume
Volume defined by: Near Plane (n) Far Plane (f) Width (W) Height (H)
For Orthographic Projection
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Tut 14.2: Rectangular Visible Volume
Experiment with
RectangularVisibleVolume
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Tut 14.2: Orthographic Projection
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
The Viewing Frustum Volume
Volume defined by: Near Plane (n) Far Plane (f) Fields of view (fov)
For Orthographic Projection
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Near Plane and Aspect Ratio
Aspect Ratio
Near Plane Height (nh) Width (nw)
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Tut 14.3: Viewing Frustum
Experiment with
Viewing Frustum
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Tut 14.3: Perspective Projection
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Tut 14.4: Near/Far Distance
Two squares very closeto each other:
Set n/f values to see errors!!
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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)
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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: SceneNode’s Transform operator! DrawHelper: Matrix Stack Manipulations!
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
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
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
The EC Orthonormal Basis Viewing Parameters: Eye Position
At PositionUp Vector
View Vector Side Vector Adjusted Up Vector:
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Example:
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
The Eye Coordinate Space
Origin: eye position Axes Directions
View: -z Up: y Side: x
Visible Volume Near: z=-n Far: z=-f
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Align EC and WC Orthonormal Basis
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
MV: Mw2e WC To EC Transform
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
Inverse Transform: Me2w
Row-4 is: The Eye Position!!
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
The MP: Projection Transform
Transform from EC to NDC Recall NDC Range:
Transform: Squeeze the View Frustum into NDC
Cube
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
View Frustum to NDC Cube
Chapter 14
Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer
3D NDC to 2D Image (Near) Plane
Resulting image on the near plane
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