CSE325 Computer Science and Sculpture

1. CSE325 Computer Science and Sculpture Prof. George Hart

2. Lecture 4 – Maya • Maya is one high-end 3D design program out of many commercially available. • It is available at Stony Brook in three CS labs and in the Art SINC site. • It has a great many capabilities, of which we will explore only a few. • This week: we make geometric forms. • Future week: organic and human forms.

3. Some Comparable Programs • Various Features: • Art vs. Engineering Design • Animation • Primitive Objects • Operators • File Formats • Rendering • Cost • Maya • Blender • Autocad • Turbocad • Rhinoceros • 3D Max • Solidworks • Form-Z • Inventor • SketchUp • Geomagic Studio • Materialize

4. Learning Maya • Long learning time if you want to master all features, but we will focus on just a few. • Representations include: • Polygonal Meshes — Our focus this week • “NURBS” • Subdivision Surfaces • Excellent built-in tutorials and help files. • You can download the free “Personal Learning Edition” to learn from. (It doesn’t save files in any standard format.)

5. Getting Started • Make sure you have the Modeling menus selected in the drop-down box at top left • Make sure you have the Polygons “shelf” tab selected. • Buttons on “shelf” create a cube, sphere, … • ALT + left, middle, or right mouse button move your point of view (the camera). • Blue buttons on left put you in mode to move, rotate, or scale a selected object.

6. Getting Started • Use the black buttons on left select Single Perspective View or Four View. • Shift+click to select multiple objects. • “4” key = Wireframe; “5” key =Shaded • When working with polyhedra, to see the facets clearly, do this: In the Shading menu of the view window, select “Flat shade all” and in “Shade Options” check “Wireframe on Shaded”

7. Exercise 1 — Play • Get familiar with primitive 3D objects: Sphere, cube, cylinder, cone, torus • Get familiar with simple operations: Move, rotate, scale, chamfer, bevel, poke; boolean union, intersection, and difference. • Handy Keyboard shortcuts: • Undo = ctrl-Z • Duplicate = ctrl-D • Delete = Del key • For menu items,  brings up an options panel. • The “channel box” at right lets you type in properties.

8. Exercise 2 — Compound of 3 Cubes The object on the left tower is a compound of three concentric cubes. To make it, create three cubes, and rotate one 45 degrees on the X-axis, rotate the second 45 degrees on the Y-axis, and rotate the third 45 degrees on the Z-axis. To get just the outer surface, take their Boolean union. M.C. Escher, Waterfall

9. Exercise 3 — Octahedron Method: Start with a 4-row, 4-wedge sphere, and keep only the six points on the axes: • Create 4,4, sphere • Right-click to change from selecting objects to selecting vertices, edges, or faces. • Delete the edges you don’t need. • Delete the vertices you don’t need. • Save your octahedron for later. (We will make it again by another technique in Exercise 5 below.)

10. Exercise 4 — Octahedron Variations Compound with cube requires proper scaling. “Stella Octangula” can be made by “poking” an octahedron

11. Octahedron Variations, Continued “Truncated octahedron” has regular hexagons. (How much chamfer?) Chamfer 50% to get “cuboctahedron”

12. Exercise 5 — Tetrahedron & Variations • Triangulate cube • Flip edges as necessary so the six diagonals of the squares are tetrahedron edges. • Delete 4 vertices not on tetrahedron with Edit Polygons | Delete vertex • (Save file for later) • Duplicate, 90 degrees rotated, to make “Stella Octangula” a new way. • Intersect two tetrahedra to make octahedron a new way.

13. Exercise 6 — Rhombic Dodecahedron • Poke cube to height which makes adjacent triangles merge into rhombi. • Delete the twelve edges of the original cube. • Poke it to make a “stellated rhombic dodecahedron”, which is the object on the right-side tower in Escher’s Waterfall.

14. Exercise 7 — Framework of Cube • Subtract from a cube three scaled cubes, to leave just the edges of the original cube. Below is the first step: You can subtract out a fourth cube so the interior of the corners looks like this:

15. Exercise 8 — Dodecahedron Intersection of 6 slabs. (“slab” = “cube” which is short along one axis.) Each slab is given a 31.7 degree rotation about some axis: • 2 X-axis slabs, rotated +/-31.7 deg along Y • 2 Y-axis slabs, rotated +/-31.7 deg along Z • 2 Z-axis slabs, rotated +/- 31.7 deg along X Then save, chamfer, bevel, and poke it:

16. Exercise 8 1/2 — Warm-up Here is another way to make the octahedron, starting from a cube. It is good practice of a technique you will use in the next exercise to make an icosahedron from the dodecahedron: • Poke cube to create a vertex in center of each face. • Edit Polygons / Texture / Merge UVs, (which allows flips in the next step). • Flip edges of original cube to become octahedron edges. This makes the stella octangula again. • Delete original cube vertices.

17. Exercise 9 — Icosahedron • Poke dodecahedron to create vertex in center of each face. • Edit Polygons / Texture / Merge UVs • Flip edges of original dodecahedron to become icosahedron edges • Delete original dodecahedron vertices. Then save, chamfer, bevel, poke:

18. Exercise 10 — Edge Models • Duplicate the form • Scale one to be 10% smaller. • Use Extrude Face tool to build out a prism on all faces of the smaller one. • Take their Boolean difference.

19. Exercise 10 — Some Ideas to Try M.C. Escher, Stars

20. More Challenges Try some of Wentzel Jamnitzer’s constructions: http://www.mathe.tu-freiberg.de/~hebisch/cafe/jamnitzer/galerie7c.html