Digital Media
Dr. Jim Rowan
ITEC 2110
Vector Graphics II
Manipulating
objects AKA closed curves
• Translation is a simple up/down side-toside movement
• Scaling: make bigger or smaller
• Rotation about a point
• Reflection about a line
Object fills
• Solid color
• Patterns
• Gradients
– linear
– radial
3-D... 3 dimensions
• x, y and z
• x & y form the ground plane
• z is the height
3-D
• Way more complex than 2-D
• 3-D shapes (objects) are defined by their
surfaces
• Made even more complicated by the fact that
a 3-D object inside the computer must be
translated into 2-D to be rendered on a
computer screen...
– This results in the need to specify the viewpoint
3-D: additional complexity
• lighting
– natural
– artificial
• atmosphere
• surface texture
• rendering is extremely computationally
expensive (demanding)
Managing Complexity
Structural hierarchy
• Things in the real world are
compositions of smaller things
• Things in the 3-D graphics world are
also compositions of smaller things
• Hierarchical structure is an excellent
way of coping with complexity
• Also seen in object-oriented
programming like Java and Squeak!
Car
Structural hierarchy
– Wheels (4)
• tire
• wheel
• hubcap
– Doors (2)
• handles
– inside
» lever
– outside
» button
» handle
• window(s)
– Lights
• headlights (2)
• tail lights (2+)
• stop lights (2+)
3-D: additional complexity
• rendering is extremely computationally
expensive (demanding)
– lighting
•
•
•
•
natural
artificial
reflections off other objects in the scene
shadows cast by other objects in the scene
– surface texture affects appearance
3D Models
3-D models
• Constructive solid geometry
– uses geometric solids: cube, cylinder,
sphere and pyramid
– objects build by squishing and stretching
those objects
– objects joined using union, intersection
and difference
3-D models
constructive solid geometry
• Union
– new object is made from the space occupied by
both objects
• Intersection
– new object is made of the space that the two
objects have in common
• Difference
new object is made from
3-D models
Free Form
• Uses an object’s surface (it’s boundary with the
world) to define it
• Build surfaces from flat polygons or curved patches
– flat polygons are easier to render and therefore frequently
used in games where computational power is limited
• Results in an object drawn as a “mesh”
• Can be done using Bezier surface patch but have 16
control points
• More tractable patch uses a surface called a nonrational B-spline
3-D models
Free Form: Extrusion
• Draw a 2 dimensional shape through
space along a line
• The line can be straight or curved
3-D models
Procedural modeling
Objects are defined by formulas
• Best known is based on Fractals
• Fractals
– exhibit the same structure at all levels of detail
– aka “self similar”
– used to model natural objects
– http://en.wikipedia.org/wiki/Fractal
• Meatballs model soft objects
• Particle systems... many particles, few controls
• Physics... distribution of mass, elasticity, optical
properties, laws of motion
3-D Rendering
• Rendering engine handles the
complexity
• Wire frames are used to preview objects
and their position
– can’t tell which surface is closer to us and
which surface is hidden
• To save computation time, hidden
surfaces are removed before rendering
3-D rendering
• Lighting
– Added to scene much like an object
– spot light, point source, floodlight...
– position and intensity
• Direct relationship between rendering
quality and computational burden
3-D rendering
• Shading... how light reacts with surface
– Based roughly on physics but modified by
heuristics
• Texture mapping
– An image is mathematically wrapped around the object
• Light reflecting off objects of one color affect
the color and lighting of surrounding objects
– Two methods
• Ray tracing Complex... must be repeated for pixel in the
image... photo-realistic results
• Radiosity
Questions?