CS 184: COMPUTER GRAPHICS

Lecture #23 -- Mo: 4/19, 1999.

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Preparation:

Read: (superficially) Ch 11.2 - 11.2.2 Parametric Cubic Curves -- Bezier Curves

Lecture Topics

Review: Splines Basics

Making smooth shapes.
Cubic polynomials.
Degrees of smoothness:
-- Parametric Continuity: differentiability of the parametric representation (C0, C1, C2, ...)
-- Geometric Continuity: smoothness of the resulting displayed shape (G0=C0, G1=tangent-cont., G2=curvature-cont. )

Cubic Bezier Curves and Hermite Splines

Basic underlying math;
Cubic Hermite Spline: 2 endpoints, 2 tangent directions.
Cubic Bezier Curve: 2 endpoints, 2 approximated intermediary control points.
Influence of parameters.
DOF's.

Properties of Bezier Curves

Cubic polynomial, true space curves
Interpolate endpoints
Approximate other two control points
End tangents defined by pairs of control points
Convex hull property
Construction by 3-fold linear interpolation
Invariant under affine transformations
Start-to-end symmetry
Infinitely differentiable
May have loops, cusps

Construction of Bezier Curves

The role of the control points.
DeCasteljau construction algorithm:
-- How to draw a Bezier curve from its control points:
-- Subdivision of a Bezier curve into two pieces that together are identical to the original one.
How to put two Bezier segments together with G1 or with C1 continuity.
How to approximate a given smooth curve with Bezier segments.

Use of Splines in your Final Projects

Smooth camera paths.
Rollercoaster tracks.
Snake bodies.
Curved smooth bodies and shells.

Some Requirements and Suggestions for Final Project

MAIN TASK:
Design and Demonstrate an Interesting Character or Fancy Machine Using SLIDE

Project should contain:
changing (articulated or deformable) creatures,
performing some controllable animation.
E.g.:
Interesting vehicles, such as backhoes or bulldozers.
Strange machinery with pistons and gearwheels.
Vehicles following roads, rollercoaster tracks.
Bugs walking over interesting terrains (fractal mountains, obstacle course).
Birds, bats, or dragons flying around obstacles or through caves.
Inchworm crawling along a curvy branch.

Note:
No shared environment will be provided.
High quality rendering is NOT the primary concern.
A clever scene composition, good movements, and interaction is the focus.

Discussion of Midterm Exam

Current Homework Assignment:

ASG#9 "Procedural Generation and Rendering"
DUE: Thursday 4/22/99, 11:59pm.
CAN BE DONE WITH YOUR PARTNER OF CHOICE !

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