3D graphics eBook - Course Materials Repository
3D graphics eBook - Course Materials Repository 3D graphics eBook - Course Materials Repository
UVW mapping 225 UVW mapping UVW mapping is a mathematical technique for coordinate mapping. In computer graphics, it is most commonly a to map, suitable for converting a 2D image (a texture) to a three dimensional object of a given topology. "UVW", like the standard Cartesian coordinate system, has three dimensions; the third dimension allows texture maps to wrap in complex ways onto irregular surfaces. Each point in a UVW map corresponds to a point on the surface of the object. The graphic designer or programmer generates the specific mathematical function to implement the map, so that points on the texture are assigned to (XYZ) points on the target surface. Generally speaking, the more orderly the unwrapped polygons are, the easier it is for the texture artist to paint features onto the texture. Once the texture is finished, all that has to be done is to wrap the UVW map back onto the object, projecting the texture in a way that is far more flexible and advanced, preventing graphic artifacts that accompany more simplistic texture mappings such as planar projection. For this reason, UVW mapping is commonly used to texture map non-platonic solids, non-geometric primitives, and other irregularly-shaped objects, such as characters and furniture. External links • UVW Mapping Tutorial [1] References [1] http:/ / oman3d. com/ tutorials/ 3ds/ texture_stealth/ Vertex In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes. Definitions Of an angle The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place. Of a polytope A vertex is a corner point of a polygon, polyhedron, or other higher dimensional polytope, formed by the intersection of edges, faces or facets of the object: a vertices''''''''''''''''facts. In a polygon, a vertex is called "convex" if the internal angle of the polygon, that is, the angle formed by the two edges at the vertex, with A vertex of an angle is the endpoint where two line segments or lines come together. the polygon inside the angle, is less than π radians; otherwise, it is called "concave" or "reflex". More generally, a vertex of a polyhedron or polytope is convex if the intersection of the polyhedron or polytope with a sufficiently small sphere centered at the vertex is convex, and concave otherwise.
Vertex 226 Polytope vertices are related to vertices of graphs, in that the 1-skeleton of a polytope is a graph, the vertices of which correspond to the vertices of the polytope, and in that a graph can be viewed as a 1-dimensional simplicial complex the vertices of which are the graph's vertices. However, in graph theory, vertices may have fewer than two incident edges, which is usually not allowed for geometric vertices. There is also a connection between geometric vertices and the vertices of a curve, its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated by a smooth curve there will be a point of extreme curvature near each polygon vertex. However, a smooth curve approximation to a polygon will also have additional vertices, at the points where its curvature is minimal. Of a plane tiling A vertex of a plane tiling or tessellation is a point where three or more tiles meet; generally, but not always, the tiles of a tessellation are polygons and the vertices of the tessellation are also vertices of its tiles. More generally, a tessellation can be viewed as a kind of topological cell complex, as can the faces of a polyhedron or polytope; the vertices of other kinds of complexes such as simplicial complexes are its zero-dimensional faces. Principal vertex A polygon vertex of a simple polygon P is a principal polygon vertex if the diagonal intersects the boundary of P only at and . There are two types of principal vertices: ears and mouths. Ears A principal vertex of a simple polygon P is called an ear if the diagonal that bridges lies entirely in P. (see also convex polygon) Mouths A principal vertex of a simple polygon P is called a mouth if the diagonal lies outside the boundary of P. (see also concave polygon) Vertices in computer graphics In computer graphics, objects are often represented as triangulated polyhedra in which the object vertices are associated not only with three spatial coordinates but also with other graphical information necessary to render the object correctly, such as colors, reflectance properties, textures, and surface normals; these properties are used in rendering by a vertex shader, part of the vertex pipeline. External links • Weisstein, Eric W., "Polygon Vertex [1] " from MathWorld. • Weisstein, Eric W., "Polyhedron Vertex [2] " from MathWorld. • Weisstein, Eric W., "Principal Vertex [3] " from MathWorld. References [1] http:/ / mathworld. wolfram. com/ PolygonVertex. html [2] http:/ / mathworld. wolfram. com/ PolyhedronVertex. html [3] http:/ / mathworld. wolfram. com/ PrincipalVertex. html
- Page 179 and 180: Screen Space Ambient Occlusion 174
- Page 181 and 182: Screen Space Ambient Occlusion 176
- Page 183 and 184: Shadow mapping 178 Algorithm overvi
- Page 185 and 186: Shadow mapping 180 Drawing the scen
- Page 187 and 188: Shadow mapping 182 Further reading
- Page 189 and 190: Shadow volume 184 There is also a p
- Page 191 and 192: Shadow volume 186 The depth fail me
- Page 193 and 194: Silhouette edge 188 Silhouette edge
- Page 195 and 196: Specular highlight 190 Specular hig
- Page 197 and 198: Specular highlight 192 normalized o
- Page 199 and 200: Sphere mapping 194 Sphere mapping I
- Page 201 and 202: Stencil codes 196 Stencil codes Ste
- Page 203 and 204: Stencil codes 198 Stencils The shap
- Page 205 and 206: Stencil codes 200 [7] Wellein, G et
- Page 207 and 208: Subdivision surface 202 used a four
- Page 209 and 210: Subsurface scattering 204 Subsurfac
- Page 211 and 212: Subsurface scattering 206 External
- Page 213 and 214: Surface normal 208 If a (possibly n
- Page 215 and 216: Surface normal 210 Normal in geomet
- Page 217 and 218: Texture filtering 212 Texture filte
- Page 219 and 220: Texture mapping 214 Texture mapping
- Page 221 and 222: Texture mapping 216 constant distan
- Page 223 and 224: Texture synthesis 218 • Structure
- Page 225 and 226: Texture synthesis 220 Pattern-based
- Page 227 and 228: Texture synthesis 222 • Micro-tex
- Page 229: UV mapping 224 A UV map can either
- Page 233 and 234: Vertex Buffer Object 228 //Make the
- Page 235 and 236: Vertex Buffer Object 230 GLuint sha
- Page 237 and 238: Vertex Buffer Object 232 vertexes *
- Page 239 and 240: Virtual actor 234 Virtual actor A v
- Page 241 and 242: Virtual actor 236 exercises, and ev
- Page 243 and 244: Volume rendering 238 Volume ray cas
- Page 245 and 246: Volume rendering 240 Maximum intens
- Page 247 and 248: Volume rendering 242 Image-based me
- Page 249 and 250: Volumetric lighting 244 References
- Page 251 and 252: Voxel 246 • Outcast, a game made
- Page 253 and 254: Z-buffering 248 Z-buffering In comp
- Page 255 and 256: Z-buffering 250 } } display COLOR a
- Page 257 and 258: Z-fighting 252 Z-fighting Z-fightin
- Page 259 and 260: Appendix 3D computer graphics softw
- Page 261 and 262: 3D computer graphics software 256
- Page 263 and 264: 3D computer graphics software 258
- Page 265 and 266: 3D computer graphics software 260 2
- Page 267 and 268: Article Sources and Contributors 26
- Page 269 and 270: Article Sources and Contributors 26
- Page 271 and 272: Image Sources, Licenses and Contrib
- Page 273 and 274: Image Sources, Licenses and Contrib
Vertex 226<br />
Polytope vertices are related to vertices of graphs, in that the 1-skeleton of a polytope is a graph, the vertices of<br />
which correspond to the vertices of the polytope, and in that a graph can be viewed as a 1-dimensional simplicial<br />
complex the vertices of which are the graph's vertices. However, in graph theory, vertices may have fewer than two<br />
incident edges, which is usually not allowed for geometric vertices. There is also a connection between geometric<br />
vertices and the vertices of a curve, its points of extreme curvature: in some sense the vertices of a polygon are<br />
points of infinite curvature, and if a polygon is approximated by a smooth curve there will be a point of extreme<br />
curvature near each polygon vertex. However, a smooth curve approximation to a polygon will also have additional<br />
vertices, at the points where its curvature is minimal.<br />
Of a plane tiling<br />
A vertex of a plane tiling or tessellation is a point where three or more tiles meet; generally, but not always, the tiles<br />
of a tessellation are polygons and the vertices of the tessellation are also vertices of its tiles. More generally, a<br />
tessellation can be viewed as a kind of topological cell complex, as can the faces of a polyhedron or polytope; the<br />
vertices of other kinds of complexes such as simplicial complexes are its zero-dimensional faces.<br />
Principal vertex<br />
A polygon vertex of a simple polygon P is a principal polygon vertex if the diagonal intersects<br />
the boundary of P only at and . There are two types of principal vertices: ears and mouths.<br />
Ears<br />
A principal vertex of a simple polygon P is called an ear if the diagonal that bridges lies<br />
entirely in P. (see also convex polygon)<br />
Mouths<br />
A principal vertex of a simple polygon P is called a mouth if the diagonal lies outside the<br />
boundary of P. (see also concave polygon)<br />
Vertices in computer <strong>graphics</strong><br />
In computer <strong>graphics</strong>, objects are often represented as triangulated polyhedra in which the object vertices are<br />
associated not only with three spatial coordinates but also with other graphical information necessary to render the<br />
object correctly, such as colors, reflectance properties, textures, and surface normals; these properties are used in<br />
rendering by a vertex shader, part of the vertex pipeline.<br />
External links<br />
• Weisstein, Eric W., "Polygon Vertex [1] " from MathWorld.<br />
• Weisstein, Eric W., "Polyhedron Vertex [2] " from MathWorld.<br />
• Weisstein, Eric W., "Principal Vertex [3] " from MathWorld.<br />
References<br />
[1] http:/ / mathworld. wolfram. com/ PolygonVertex. html<br />
[2] http:/ / mathworld. wolfram. com/ PolyhedronVertex. html<br />
[3] http:/ / mathworld. wolfram. com/ PrincipalVertex. html
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