CIS 681

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CIS 681

• Introduction to 3D Image Generation

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Computer graphics is the creation and
manipulation of graphics images by means of
computer. (Marc Berger, 1986.)
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Vector Graphics

• Draw a picture one line at a time.

• Drawbacks
• Wireframe.
• Must continually redraw all objects.

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Raster Graphics

• n x m grid of pixels

• Problems
• Convert objects to pixels
• Aliasing Screen resolution may be much less than
  object resolution.

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Raster Graphics
Raster Graphics
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Scan Conversion

• Transform 3d object into 2d object
• Scan 3d object, converting it into pixels.

• Fast
• Commonly used
• Industry standard OpenGL
• Hardware support (OpenGL).

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Ray Tracing

• Shoot a ray through each pixel
• Find first object intersected by ray.

Image plane
Eye

• Slow
• Not commonly used
• No hardware support.

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Ray Tracing vs. Scan Conversion

• Scan Conversion
• (CIS 581, 781, )
• Fast
• Commonly used
• Industry standard (OpenGL)
• Hardware support.

• Ray Tracing
• (CIS 681)
• Models light (better)
• Photorealistic rendering
• Special effects
• Better for understanding rendering/lighting.

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Creating a Scene

• Translate rotate objects.
• Linear algebra. (Prerequisite Math 568 or 571.)

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Ray Tracing

• Shoot a ray through each pixel
• Find first object intersected by ray.

Eye

• Compute ray. (More linear algebra.)
• Compute ray-object intersection.

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Example
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Diffuse Reflection

• Calculate amount/color of light shining on an
  object.
• Depends on angle between light ray and surface
  normal.

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Example Diffuse reflection
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Specular Reflection

• Calculate light bouncing off object to your eye
• Angle of incidence angle of reflection.

Angle of incidence
Angle of reflection
Eye
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Example Specular Reflection
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Whats wrong with this picture?
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Shadows

• Determine when light ray is blocked from reaching
  object.

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Reflection
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Transparency
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Transparency Refraction
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Recursive Ray Tracing
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Polyhedral Models
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Texture Mapping
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Sampling and Aliasing

• Problem Representing pixel by a single ray.

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Anti-Aliasing

• Solution
• Use multiple rays
• Average values calculated by rays.

Image plane
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Sampling and Aliasing

• Problem Sampling frequency may match image
  frequency.

Image plane
Eye
Viewport
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Random/Stochastic Sampling

• Randomly sample rays through pixel.

Image plane
Eye
Viewport
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Efficiency

• 1280 x 1024 1,310,720 ? 106 pixels.
• 106 initial rays.
• 106 reflection rays.
• Potentially 106 refraction rays.
• 3 x 106 shadow rays (3 lights.)
• Next level
• Potentially 4 x 106 refraction/reflection rays.
• 1,000,000 polygons.
• 107 x 106 1013 ray-polygon intersection
  calculations.

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Intersection Data Structures

• Bounding boxes
• Spatial subdivision.

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Bounding Boxes
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Spatial Subdivision
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Major Course Topics

• Object coordinate transformations.
• Ray-object intersections.
• Diffuse specular reflection.
• Shadows.
• Opacity refraction.
• Shadows.
• Recursive ray tracing.
• Polyhedral models.
• Texture mapping.
• Polyhedral models.
• Anti-aliasing and sampling.
• Bounding boxes and spatial subdivision.