This document outlines the course objectives for an introduction to 3D modeling and visualization class. The course will be taught on Tuesdays from 6-9pm for 3 credits. Topics that will be covered include NURBS surfaces, topology, Riemannian manifolds, the Moebius strip, Klein bottle, thickening surfaces, the human ear, dissection, and the work of Andreas Vesalius. The goal is to move from basic surface modeling to modeling anatomical structures.
1 of 34
Downloaded 19 times
More Related Content
topology of surface
1. Pratt Institute _School of Architecture _Sensation Tectonics
Arch 522C.09/.10: _Introduction to 3D Modeling and Visualization
_Instructor: _Robert Brackett
_Robert.Brackett3@gmail.com
_Instruction: _Tuesdays , 6:00 – 9:00
_Credits: _03
_Classification: _Elective
6. Topology _the nurbs surface
_Manifolds
_Riemannian Manifolds
To measure distances and angles on manifolds, the manifold must be
Riemannian. A Riemannian manifold is a differentiable manifold in
which each tangent space is equipped with an inner product 〈⋅,⋅〉
in a manner which varies smoothly from point to point. Given two
tangent vectors u and v, the inner product 〈u,v〉 gives a real
number. The dot (or scalar) product is a typical example of an inner
product. This allows one to define various notions such as length,
angles, areas (or volumes), curvature, gradients of functions and
divergence of vector fields.
11. Topology _the Klein Bottle
_ A Klein Bottle is a 4-Dimensional topography that cannot be
embedded within 3-Dimensional space. The surface has some
very interesting properties, such as being one-sided, like the
Moebius strip; being closed, yet having no "inside" like a torus
or a sphere; and resulting in two Moebius strips if properly cut
in two.