Building Models. Objectives. Introduce simple data structures for building polygonal models. OpenGL vertex arrays. Vertex lists Edge lists
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1 Building Models Objectives Introduce simple data structures for building polygonal models Vertex lists Edge lists OpenGL vertex arrays 2
2 Representing a Mesh Consider a mesh v 5 v e e e 3 v v e 4 e v e v 7 7 e v e 2 2 e 2 e 0 e 4 e 5 v 3 8 nodes and 2 edges 5 interior polygons interior (shared) edges Each vertex has location v i = (x i y i z i ) 3 Simple Representation Define each polygon by geometric locations of vertices Leads to OpenGL code such as glbegin(gl_polygon); glvertex3f(x, y, z); glvertex3f(x, y, z); glvertex3f(x7, y7, z7); glend(); Inefficient and unstructured Consider moving vertex to new location Must search for all occurrences 4 2
3 Inward and Outward Facing Polygons Order {v, v, v 7 } and {v, v 7, v } equivalent ==> same polygon rendered by OpenGL but {v, v 7, v } different First two ==> outwardly facing polygons Use right-hand rule = counter-clockwise encirclement of outward-pointing normal OpenGL can treat inward and outward facing polygons differently 5 Geometry vs Topology Good idea to look for data structures that separate geometry from topology 3
4 Geometry vs Topology Good idea to look for data structures that separate geometry from topology Geometry: locations of vertices Topology: organization of vertices and edges Example: polygon = ordered list of vertices edge connecting successive pairs of vertices last to first Topology holds even if geometry changes 7 Vertex Lists Put geometry in array Use pointers from vertices into this array Introduce polygon list P P2 P3 P4 P5 topology v v 7 v v 8 v 5 v geometry x y z x 2 y 2 z 2 x 3 y 3 z 3 x 4 y 4 z 4 x 5 y 5 z 5. x y z x 7 y 7 z 7 x 8 y 8 z 8 8 4
5 Shared Edges Vertex lists will draw filled polygons correctly but if draw polygon by its edges ==> shared edges drawn twice Can store mesh by edge list 9 Edge List e e2 e3 e4 e5 e e7 e8 e9 v v x y z x 2 y 2 z 2 x 3 y 3 z 3 x 4 y 4 z 4 x 5 y 5 z 5. x y z x 7 y 7 z 7 x 8 y 8 z 8 v v 8 v 5 e e 8 e 3 e v e v 7 7 e v e 2 2 e 2 e 9 e 5 e 0 Note polygons are not represented v 3 e 4 0 5
6 Modeling a Cube Model color cube for rotating cube program Define global arrays for vertices and colors GLfloat vertices[][3] = {{-.0,-.0,-.0},{.0,-.0,-.0}, {.0,.0,-.0}, {-.0,.0,-.0}, {-.0,-.0,.0}, {.0,-.0,.0}, {.0,.0,.0}, {-.0,.0,.0}}; GLfloat colors[][3] = {{0.0,0.0,0.0},{.0,0.0,0.0}, {.0,.0,0.0}, {0.0,.0,0.0}, {0.0,0.0,.0}, {.0,0.0,.0}, {.0,.0,.0}, {0.0,.0,.0}}; Drawing a polygon from a list of indices Draw quadrilateral from list of indices into array vertices and use color corresponding to first index void polygon(int a, int b, int c, int d) { glbegin(gl_polygon); glcolor3fv(colors[a]); glvertex3fv(vertices[a]); glvertex3fv(vertices[b]); glvertex3fv(vertices[c]); glvertex3fv(vertices[d]); glend(); } 2
7 Draw cube from faces void colorcube( ) { polygon(0,3,2,); polygon(2,3,7,); polygon(0,4,7,3); polygon(,2,,5); polygon(4,5,,7); polygon(0,,5,4); } Note that vertices are ordered so that obtain correct outward facing normals 3 Efficiency Weakness of approach: building model in application ==> many function calls to draw cube Drawing cube by its faces in most straightforward way requires glbegin, glend glcolor 24 glvertex More if use texture and lighting 4 7
8 Vertex Arrays OpenGL provides facility called vertex arrays ==> allows to store array data in implementation Six types of arrays supported Vertices Colors Color indices Normals Texture coordinates Edge flags Will need only colors and vertices 5 Initialization Using same color and vertex data, first enable glenableclientstate(gl_color_array); glenableclientstate(gl_vertex_array); Identify location of arrays glvertexpointer(3, GL_FLOAT, 0, vertices); 3d arrays data array stored as floats data contiguous glcolorpointer(3, GL_FLOAT, 0, colors); 8
9 Mapping indices to faces Form array of face indices GLubyte cubeindices[24] = {0,3,2,,2,3,7, 0,4,7,3,,2,,5,4,5,,7,0,,5,4}; Each successive four indices describe face of cube Draw through gldrawelements ==> replaces all glvertex and glcolor calls in display callback 7 Drawing the cube Method : what to draw number of indices for(i=0; i<; i++) gldrawelements(gl_polygon, 4, GL_UNSIGNED_BYTE, &cubeindices[4*i]); format of index data Method 2: start of index data gldrawelements(gl_quads, 24, GL_UNSIGNED_BYTE, cubeindices); Draws cube with function call!! 8 9
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