1. COMPUTER GRAPHICS CS 482 – FALL 2015 SEPTEMBER 10, 2015 TRIANGLE MESHES 3D MESHES MESH OPERATIONS

2. 3D MESHES CS 482 – FALL 2015 TRIANGLES VERSUS QUADRILATERALS SEPTEMBER 10, 2015: TRIANGLE MESHESPAGE 67 3D SHAPES ARE USUALLY REPRESENTED IN GRAPHICS SYSTEMS WITH POLYGONAL MESHES. TRIANGLE MESHES AND QUADRILATERAL MESHES ARE MOST COMMONLY USED. TRIANGLE MESH ADVANTAGESQUAD MESH ADVANTAGES TRIANGLES ARE ALWAYS PLANAR, QUADS ARE NOT IT’S EASIER TO TILE A SURFACE WITH TRIANGLES OF A UNIFORM SIZE IT’S EASIER TO MODEL THE CONTOURS OF A 3D SURFACE WITH QUADS IT’S EASIER TO MAP TEXTURES TO QUADS THAN TO TRIANGLES

3. 3D MESHES CS 482 – FALL 2015 MANIFOLD MESHES SEPTEMBER 10, 2015: TRIANGLE MESHESPAGE 68 A MESH IS A MANIFOLD IF IT SATISFIES THE FOLLOWING TWO CONDITIONS: 1.EACH EDGE IN THE MESH IS INCIDENT WITH ONLY ONE OR TWO FACES 2.THE FACES INCIDENT TO EACH VERTEX FORM EITHER AN OPEN OR A CLOSED FAN OPEN FAN CLOSED FAN

4. 3D MESHES CS 482 – FALL 2015 TRIANGLE ORIENTATION SEPTEMBER 10, 2015: TRIANGLE MESHESPAGE 69 TRIANGLE MANIFOLD MESHES LEND THEMSELVES TO ORIENTATION, WHICH FACILITATES THE DETERMINATION OF CONSISTENT REFERENCES TO THE “INSIDE” AND “OUTSIDE” OF POLYHEDRAL SURFACES. START BY ORDERING THE VERTICES OF ANY TRIANGLE IN THE MESH. FOR EACH SHARED EDGE, ORDER THE VERTICES OF EACH ADJACENT TRIANGLE SO THE SHARED EDGE’S VERTICES ARE IN THE OPPOSITE ORDER. CONTINUE, ONE ADJACENT TRIANGLE AT A TIME, UNTIL THE ENTIRE MESH HAS BEEN ORIENTED.

5. 3D MESHES CS 482 – FALL 2015 TRIANGLE ORIENTATION EXAMPLE SEPTEMBER 10, 2015: TRIANGLE MESHESPAGE 70 NOTE THAT THE COUNTERCLOCKWI SE ORIENTATION OF EACH TRIANGLE YIELDS NORMAL VECTORS (VIA THE CROSS PRODUCT) THAT ALL POINT EXTERIOR TO THE POLYHEDRON.

6. MESH OPERATIONS CS 482 – FALL 2015 EDGE COLLAPSE SEPTEMBER 10, 2015: TRIANGLE MESHESPAGE 71 MESH SIMPLIFICATION IS A CLASS OF ALGORITHMS THAT TRANSFORMS A MESH INTO ONE WITH FEWER VERTICES, EDGES, AND FACES, REDUCING ITS COMPLEXITY WHILE PRESERVING CERTAIN PROPERTIES (E.G., GEOMETRIC DISTANCE, VISUAL APPEARANCE). AB M BA WITH EDGE COLLAPSE, AN EDGE IS REMOVED AND ITS ENDPOINTS ARE MERGED INTO A SINGLE VERTEX. THE DETERMINATION OF THE MERGED VERTEX’S POSITION MAY SIGNIFICANTLY IMPACT THE LOCAL APPEARANCE OF THE SIMPLIFIED MESH. MERGING TO ONE ENDPOINT MERGING TO THE OTHER ENDPOINT MERGING TO THE MIDPOINT

7. MESH OPERATIONS CS 482 – FALL 2015 EDGE SWAP SEPTEMBER 10, 2015: TRIANGLE MESHESPAGE 72 MESH BEAUTIFICATION IS A CLASS OF ALGORITHMS THAT TRANSFORMS A TRIANGULAR MESH INTO ONE WITH NEAR-EQUILATERAL TRIANGULAR FACES AND/OR A NEAR UNIFORM DISTRIBUTION OF VERTICES, IN ORDER TO ELIMINATE IRREGULARITIES IN THE APPEARANCE OF THE ORIGINAL MESH. Aspec t Ratio: 11 DETERMINE THE TRIANGULAR FACE WITH THE LARGEST ASPECT RATIO (THE CIRCUMSCRIBED RECTANGULAR BOUNDING BOX WITH THE LARGEST LENGTH-TO-WIDTH RATIO) DETERMINE THE LARGEST EDGE OF THAT TRIANGLE AND FIND THE OTHER TRIANGULAR FACE THAT SHARES THAT EDGE SWAP THAT EDGE WITH THE OTHER EDGE THAT SERVES AS A DIAGONAL FOR THAT TWO-TRIANGLE QUADRILATERAL