Design Realization lecture 2 John Canny 8/28/03

Last Time  Design Realization about the creation of “smart” and often networked artifacts.  Goal is fluency in several design media, (3d shape, animation, mechatronics, optics), and interdisciplinary collaboration skills.  Class consists of short exercises, contributions to the knowledge repository, and a longer project.

Updates  Class home page is  Class swiki (password needed) is up at kettle.cs.berkeley.edu/DesignRealization2 please submit summaries there by next Tues. kettle.cs.berkeley.edu/DesignRealization2  Maya will be available on some machines in HMMB but also on CD for personal class use.  First Maya assignment will go out next Tuesday – due in two weeks.

Section 1: 3D Shape  We start by listing some qualities of 3D shape (exercise):

Section 1: 3D Shape  We start by listing some qualities of 3D shape (exercise):  Try enumerating “good” shapes (natural and artificial):

3D Shape Creation  Since most people lack 3D input devices, Its usually best to work mostly with 2D shapes (curves) and “lift” them to 3D.  The 2D shape can remain an efficient way to edit the 3D shape.  c.f. McCullough’s notion of “grain” – how?

Curve Creation  Three ways in Maya:  Freehand drawing  Setting control points (not on the curve)  Setting curve points  All 3 actually produce NURB curves (Non- Uniform Rational B-splines)

Curves  Curves have tangents at every point, that define the curve’s direction.  A tangent is the straight line which is the limit of curves formed by “zooming in” to the point.  Polygonal lines have abrupt changes in tangent at vertices. Spline curves (e.g. NURBS) allow smooth tangents from one curve segment to the next (sketch).

Curves  Most 3D systems use parametric curves.  Parametric curves have a single parameter that varies along the curve, usually from 0 to 1.  Parameters make it easy to compute tangent curves, and to walk along the curve (e.g. for displaying it).

3D geometry  3D worlds are defined by 3 (cartesian) coordinates X, Y, and Z.  For historical reasons, in most 3D systems, Y is “up” and Z is toward the viewer.  These three directions also define three standard views of objects. In addition, there is usually a perspective or orthographic view from a general camera position.

3D geometry  A 3D shape has six degrees of movement freedom:  3 degrees of translation along X, Y, Z  3 degrees of rotation about X, Y, Z

3D puzzle  In Maya, the six degrees of freedom are mapped to mouse movement (two DOF), with one of 3 mouse buttons down (a total of six). BUT…  Mouse middle allows translation in X, Y.  Mouse right allows translation only in Z.  Mouse left allows all three rotational DOF.  In other words, one mouse DOF is wasted, and we get all 6 motion DOFs from 5 mouse DOFs. How??

Resources to answer this question  Good books: Hearn and Baker “Computer Graphics (C version), Prentice-Hall  Links:  JFC’s notes: JFC/past courses/CS184  Laura Down’s notes on quaternions  Discussion: relate this to McCullough’s notion of direct vs. indirect manipulation.

3D surfaces  NURB surfaces are built from NURB curves, and smoothly skin between them.  Surfaces are also parametric, with two parameters this time (u, and v), typically between 0 and 1.  Each surface point has two tangents (one each along u and v directions), and a normal which is off the surface.

Continuity and degree  The default NURBs in Maya have (algebraic) degree 3. A curve has degrees of freedom as well (sketch).  The higher the algebraic degree, the more degrees of freedom the curve has.  Higher degrees of freedom allow higher degrees of smoothness (or continuity) between curve segments.

Continuity and appearance  High continuity is important for appearance of smooth, glossy surfaces. Automotive models may need 4 th order or higher continuity.  Other properties, especially curvature, may be limited by the fabrication process.

Resources again  Good books on graphics: Hearn and Baker “Computer Graphics (C version), Prentice-Hall  Links:  JFC’s notes: JFC/past courses/CS184  The “Maya 4.5 Bible”

Wrap-up  Finish the Itten and McCullough readings.  Write short summaries (< 1 page), and post to Swiki by next Tuesday. Wait ‘til tomorrow for submission page.  Maya CDs should be available on Tuesday next week, when the assignment will go out.