Pratt Institute _School of Architecture _Sensation TectonicsArch 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

Topology_the nurbs surface_Non Uniform Rational B-Splines

Topology_the nurbs surface

Topology_design

Topology_the nurbs surface_Continuity & Patches

Topology_the nurbs surface_Manifolds

_Riemannian ManifoldsTo 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.

Topology_the nurbs surface

Topology_the nurbs surface

Topology_the Moebius Strip

Topology_the Moebius Strip

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.

Topology_the Klein Bottle

Topology

Topology_Thickening the Surface

Topology_Thickening the Surface

Topology_The Human Ear

Topology_The Human Ear

Topology_The Human Ear

The Dissected Body

Topology_from Surface to Flesh

Topology_Andreas Vesalius

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh

Flesh