Intro or, Who Am I, and What Am I Doing Here? References The ETGG1803 slides of Dr. James Hudson Chapter 2

This Class Who? You! The 3D Jedi (or aspiring Padawan, as the case may be...) What? Making the leap from 2D to 3D How? Math. Lots and lots of math. "Mathematics is the language with which God has written the universe."–Galileo Galilei  There's going to be a lot of math in this class!  Everything we see → Modeled with math!

2D Objects Vector drawings Bitmap drawings “Super Meat Boy”, © 2008, 2010 Team Meat

3D Objects Analytic Surfaces (Spheres, planes, boxes, etc) Polygonal Surfaces Other choices:  Spline surfaces  Metaballs (not meatballs!)  Voxels ……

Goals of the class Trig review and more applications Linear Algebra – Vectors and Matrices (as they apply to 3d graphics) Intro to 3D graphics – Raytracer: 3D objects (analytic surfaces, mostly) => 2D image heavily vector-based slow, high-quality rendering – Rasterizer: 3D objects (polygons, mostly) => 2D image heavily matrix-based faster, lower-quality rendering of a scene. – Lighting and Shading

Coordinate Systems Simplest: 1D Origin Axis direction scale Specify location in a 1D C.S.: Just a number Ex:

Another 1D C.S. Just drawn differently Where we draw the point 2.4 depends on Origin Axis (and its scale) No such thing as an absolute position – position depends on the frame of reference

2D Coordinate Systems

3D Math 3 axes: commonly named x, y, and z Question: Which way does z go? x y Z?

Handedness LHS vs. RHS x y z x y z

Right-Hand Rule Thumb, Index finger, Middle finger Also works for left handed space x y z x y z

Scalars and Vectors A scalar is a single number. A vector is a group of scalars. For now, think of this as a point. In 1-d space, a point is just a scalar. In 2-d space, a point is a group of 2 scalars. In 3-d space, a point is a group of 3 scalars. In 4-d space, a point is a group of 4 scalars. … In 1000-d space, a point is a group of 1000 scalars. … In N-d space, a point is a group of N scalars.