CSC 220 3D Computer Graphics Fall 2003

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CSC 220 3D Computer Graphics Fall 2003
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Graphics Hardware

• Text Mode Characters (2K bytes)
• Graphics Modes Pixels (millions of bytes)
• x-y coordinate system
• Raster Scan with Frame Buffer (aliasing)
• Vector Scan with Display List

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Color for Computer Graphics

• Red, Green, Blue phosphors and shadow mask
• VGA 640 x 480 with 16 colors
• VGA 320 x 200 with 256 colors, using the
• Color LookUp Table (CLUT) 8 bits / pixel is
• 256 colors at one time, but 262,144 colors in
  palette
• SVGA with True Color 800 x 600 (or more), using
• 24 bits / pixel millions of colors
  simultaneously

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Graphics Software

• BASIC is an exception
• APIs, or libraries
• Borland Graphical Interface (BGI)
• Graphical Kernel System (GKS)
• OpenGL

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Graphics File Formats

• GIF
• JPEG
• BMP
• TIFF
• Targa

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The Graphics Pipeline

• Modeling geometry of an object
• Viewing how the object appears
• hidden surfaces
• synthetic camera
• Rendering realism and more
• lighting
• shading
• textures
• shadows

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Modeling Techniques

• Polygons (Triangles)
• Splines (NURBS)
• Constructive Solid Geometry (CSG)
• Fractals

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Teddy a Modeling Applet

• Simple and quick
• For rough models instantly
• Spherical topology
• Operations
• creation
• extrusion
• cutting
• bending

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TERA

• A tool for visual literacy
• Can display 500,000 combinations of images
  rendered by various methods
• Can be used in two ways
• explore rendering effects
• self-test rendering effects
• Contains POV-Ray files also

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Some Visual Cues

• Visibility
• Shadows
• Reflections
• Refraction

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Surface Algorithms

• Visibility
• wireframe ambiguity
• hidden lines / surfaces
• Rendering techniques (2 of many)
• z-buffer
• ray tracing

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Some Minimal Mathematics

• 3D coordinates x,y,z as LHS
• Vectors direction and magnitude
• Normal vector to a surface
• Culling back faces

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The Z-buffer Method

• Along with frame buffer have a z-buffer
• Frame buffer holds color value for the pixel
• Z-buffer holds z value for the pixel location
• Scan each surface in succession. If z value for
  this location on this surface is less than value
  in z-buffer, replace color in frame buffer and
  update value in z-buffer
• Most common rendering method, often with special
  hardware

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POV-Ray

• No modeling, uses Scene Description Language
  (SDL)
• Does viewing and rendering
• No books in print, but excellent on-line
  documentation
• Exercises from TERA text
• render gold.pov, p.9
• render room.pov, p.20
• revise camera orientation of room, pp.21,22

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Specifying an Image in SDL

• Objects
• Simple shapes
• CSG objects
• Advanced shapes
• Transformations
• Texture
• Camera
• Lighting

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Simple Shapes

• Spheres
• Boxes
• Cones
• Cylinders
• Planes

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Constructive Solid Geometry

• Union
• Intersection
• Difference
• Merge

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Transformation of Coordinates

• Affine transformations
• translation
• scaling
• rotation
• Composition of affine transformations
• Properties of affine transformations
• straight lines stay straight
• parallel lines stay parallel
• angles do NOT stay fixed, except for rigid
  transformations (no scaling)

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Z-Buffer Shading

• Constant Shading color computed once for entire
  object
• Faceted Shading color computed once for each
  polygon
• Gouraud Shading color computed using vertex
  normal, then double interpolation of color values
  in the polygon
• Phong Shading double interpolation of vertex
  normals, then color value computed for each
  interpolated vector value in the polygon

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Lights in POV-Ray

• Point lights
• Spotlights
• radius
• falloff
• tightness
• adaptive
• jitter
• Cylinder lights (same parameters as spotlight)
• Area lights
• Ambient lighting

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Reflected Light

• When light strikes a surface, some colors are
  absorbed, and we see the colors that are
  reflected.
• We deal with three types of reflections
• ambient reflected light
• diffuse reflected light
• specular reflected light (Phong illumination)
• Computing the reflected values requires that
  vectors must be multiplied.

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Ray Tracer Shading

• Multiple reflections
• Transparency
• Refraction
• Shadows

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2D Texture Mapping

• Map Types
• planar normal parallel to X, Y, or Z
• cylindrical rotation around X, Y, or Z
• spherical rotation around X, Y, or Z
• box normal parallel to X, Y, or Z
• Problems
• poles
• distortion
• aliasing
• Bilateral symmetry and planar maps

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3D Texture Mapping

• Procedural texture is function f(x,y,z)
• Common textures are stripes, rings, ramps
• Noise for realistic effects
• amplitude
• frequency
• use of higher order terms
• eccentricity, tilt, and twist
• Texture functions in POV-Ray for glass, metal,
  stone, and wood

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Viewing the Synthetic Camera

• World Coordinates (WC) x,y,z
• r is location of camera in WC
• The View Plane U,V,N
• N is where camera is looking
• V is up direction, orthogonal to N
• U is 3rd axis, orthogonal to both N and V

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Light and its Perception

• In describing the effects of light we must take
  into account both physics and physiology.
• The wavelength of visible light varies from 400
  nanometers (violet) to 700 nanometers (red).
• In describing the quality of light, we need three
  parameters
• hue the dominant wavelength
• intensity (physics) or brightness (physiology)
• saturation the purity of the hue

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The Human Eye

• The eye has rods that are very sensitive to light
  versus dark (about 1 photon), and cones that are
  less sensitive to level (about 5 photons) but can
  distinguish colors.
• There are cones sensitive to blue, to green, and
  to red. They are all in the fovea (1/4 mm), and
  are the basis of the tristimulus theory of
  vision.
• Light which is a mixture of red and green looks
  just as yellow as does pure yellow light! The
  human visual system cannot detect overtones and
  harmonics as does the human auditory system.

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The Color Cubes

• The primaries for additive (emitted) color in
  computer graphics are red, green, and blue,
  yielding the RGB color cube.
• red green yellow
• red blue magenta
• green blue cyan
• The primaries for subtractive (reflected) color
  are cyan, magenta, and yellow, yielding the CMY
  color cube.
• cyan ink absorbs red
• magenta ink absorbs green
• yellow ink absorbs blue

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The HSV Color System

• It is difficult to predict what a given mixture
  of RGB levels will look like.
• For such a purpose, it is easier to use the HSV
  coordinate system based upon Hue, Saturation, and
  Value.
• This maps to a cone or a six-sided pyramid
• Hue is the angular location on the side wall
• Saturation is the relative distance from the
  center line to the color point (purity)
• Value is the height in the inverted cone
• These can easily be thought of in more natural
  terms such as tints, shades, and tones.

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Halftoning

• When there are a limited number of color levels
  available in the output, we can trade spatial
  resolution for color resolution. Thus, there may
  be just 2 color levels (e.g. black or white).
  Take super-pixels of size 2x2 or 3x3. Within a
  2x2 block, there are 4 individual pixels that may
  or not be lit, for 5 levels of aggregate
  intensity in that super-pixel.
• To the eye, the increased color gradation is well
  worth the loss in spatial resolution.

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Some Advanced Shapes

• Blobs for lumpy objects
• Splines to fit to control points
• approximation Bezier curves
• interpolation many types of splines
• piecewise polynomial sections (cubics)
• smoothness, or continuity
• NURBS Non Uniform Rational B Splines

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NURBS

• Non-uniform rational B-splines
• non-uniform spacing of control points
• rational a quotient (ratio) of polynomials
• also knots where kinks are desired
• NURBS are good for modeling curves
• Just as important properties are maintained
• with affine transformations, so are NURBS
  maintained under projective transformations
• so only control points need be transformed.
• NURBS can model conic sections exactly!

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The Rhino Interface

• Rhino is a modeling tool has primitive shading
  and rendering capability
• 3 Orthographic Viewports
• top, front, right views are default
• bottom, back, left views are also possible
• 1 Perspective Viewport
• 2 Toolbars, with flyouts

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Viewing in Rhino

• Parallel or perspective projection
  (each viewport)
• Panning
• Rotating
• Zooming
• zoom dynamic
• zoom extents
• zoom window
• zoom selected

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Drawing Lines

• Line segments versus polylines
• Coordinate systems
• absolute cartesian 3,4
• relative cartesian r3,4
• absolute polar 5
• relative polar r5

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Modeling Aids

• Snap to grid
• Ortho
• Object Snaps
• Layers
• Constraints
• distance constraint 5
• angle constraint

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Editing Objects

• Split and Trim
• Join and Explode
• Fillet
• Chamfer
• Transforms
• scale
• rotate
• mirror

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Rhino Geometry

• Points
• Curves
• Surfaces
• Polysurfaces blended surfaces
• Solids closed polysurfaces

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Creating Curves

• Free-form
• control points Bezier curves
• (for approximation)
• interpolate points spline curves
• (for interpolation)
• sketch
• Conic sections
• Polygons

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Creating Surfaces

• From points
• From curves
• Extrusion
• Lofting
• Revolves
• Rail sweeps

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Creating Solids

• Box
• Sphere
• Cylinder
• Tube
• Cone
• Ellipsoid
• Torus

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Technical Side of Animation

• The Storyboard
• Keyframes
• Inbetween frames
• for shape (morphing)
• for motion
• Motion capture
• Physical modeling

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Artistic Side of Animation

• Stretch and Squash
• Timing
• Anticipation
• Staging
• Slow In and Out
• Emotion