# CS 511: Topics In Computer Graphics

## Objectives

• Provide understanding of the techniques, mathematical concepts, and algorithms used in warping, morphing, and texturing, in geometric modeling, and in animation (so as to facilitate further study in the area of computer graphics).
• Provide pointers into the literature and exercise a team project based on a literature search and one or more research papers.
• Practice software implementation of different concepts and techniques covered in the course.
• Utilize graphics and scientific tools for relevant software implementation.

## Prerequisites

• CS 411, Linear Algebra.

## Syllabus

• Introduction
• Overview of the course.
• Overview of numerical tools.
• Introduction to graphics programming with OpenGL.
• Spatial transformations
• Homogeneous representations of lines and points, ideal points and the line at infinity, projective planes, duality principle.
• Euclidean, affine, perspective, bilinear, and polynomial transformations.
• Scanline algorithms
• Incremental algorithms.
• Two-pass transforms.
• Separable mappings.
• Warping and morphing
• Plane and spatial warping.
• Warping and morphing of images.
• Parameter and feature-based warping.
• Control-lines based warping.
• Texture mapping, image mosaics, and image-based rendering.
• Surface interpolation
• Intrinsic, explicit, implicit, parametric representations.
• Conic curves and quadric surfaces.
• Linear interpolation.
• Barycentric coordinates.
• Surface patches.
• Bilinear, lofted, and Coons surfaces.
• Biquadratic and bicubic surface patches.
• Catmull-Rom surfaces.
• Bezier and B-spline surfaces
• Tensor product patches.
• DeCasteljau algorithm.
• Blossom.
• Bernstein form.
• Bezier surfaces.
• B-spline surfaces.
• Polygonal techniques
• Representations of polygonal surfaces.
• Polygonal mesh reconstruction, simplification, and smoothing.
• Mesh subdivision.
• Local surface geometry estimation.
• 3D Rotation
• Quaternions, spherical linear interpolation.
• Kinematic modeling
• Forward kinematics.
• Articulated object animation.
• Denavit-Hartenberg notation.
• Inverse kinematics.
• Particle dynamics
• Integral curves.
• Phase space.
• Cloth and fur energy functions.
• Rigid body dynamics
• Orientation and angular velocity.
• Rigid body motion equations.

Edited March 2006 (html, css checks)