Texture Mapping Presented by POTLURI,KIRAN

Introduction Texture : A detailed pattern that is repeated many times to tile the plane. Texture mapping is a powerful technique for adding realism to a computer-generated scene.

Texture Mapped on to Tea Pot

Introduction (contd..) The First use of texture was developed by Catmull in the year Algorithm is applied to bicubic parametric patch model, since the parametric patch models already possesses the U,V values everywhere on its surface.

How is texture mapping done Two Dimensional Texture Mapping :: Texture Space T(u,v) Object Space (x,y,z) Screen Space (Xs,Ys) surface parameterization Projection

Algorithm The Algorithm divides the surface patch in object space. At the same time, executes subdivision in texture space. Patch subdivision proceeds until it ends in single pixel. After it reached this point, Subdivision process terminates. The required texture value for each pixel is obtained from texture domain.

Difficulties Two difficulties 1. Inventing suitable surface parameterization 2. Anti-aliasing.

Types of Texture Mapping Two Types 1. Forward texture mapping computing 3D positions of the texture points and then projecting them onto the image plane. 2. Inverse texture mapping selecting every pixel in the image plane and finding what point of the texture plane is projected there.

Drawbacks Forward Texture mapping : Adjacent texture points may project onto non adjacent image points, thus creating a non colored area.

Drawbacks Inverse Texture Mapping : Aliasing would appear, if sampling the texture map is done at a frequency higher than its Nyquist rate. Nyquist rate :the minimum theoretical sampling rate.

Polygon Mesh Texture Mapping It is also called Two-part texture mapping Introduced by Bier and Sloan Year The texture is mapped onto an intermediate surface before being mapped onto the object

How this Method Works Step 1 : mapping from two-dimensional texture space – simple three dimensional intermediate surface. e.g. : cylinder, sphere. T(u,v)  T’(x i,y i,z i ) This is know is S-mapping.

Mapping to sphere or cylinder S cylinder :: ( ,h)  (u,v) = (r/c(  -  o ),1/d(h-h o )) S sphere :: ( ,  )  (u,v) = (2q/1+(1+p 2 +q 2 ) 1/2, (2q/1+(1+p 2 +q 2 ) 1/2 ) P=tan(  )cos(  ) q= tan(  )sin(  )

O-mapping Step 2 : Mapping from 3-dimensional texture pattern onto object surface. T’(x i,y i,z i )  O(x w,y w,z w ) This is know as O-mapping.

Map to object surface There are four possible ways 1. The intersection of the reflected view ray with intermediate surface View point Intermediate surface (x i,y i,z i ) (x w,y w,z w )

Map to object surface(Contd..) 2. The intersection of the surface normal at (x,y,z) with the intermediate surface. Intermediate surface (x i,y i,z i ) (x w,y w,z w )

Map to object surface(Contd..) 3. The intersection of a line through (x,y,z) and object centroid with intermediate surface. Intermediate surface (x i,y i,z i ) (x w,y w,z w )

Map to object surface(Contd..) 4. The intersection of line from (x,y,z) to T’ whose orientation is given by surface normal at (x i,y i,z i ) Intermediate surface (x i,y i,z i ) (x w,y w,z w )

Applications

Molecular Graphics Isocontouring of the hydrophobic potential on the solvent-accessible surface of Gramicidin A

Molecular Graphics Solvent-accessible surface of ethanol, color coded against the electrostatic potential, using the traditional color coding (left) and using texture mapping (right).

Molecular Graphics The 13,767 spheres of a hydrated phospholipid bilayer (DLPE), part of a cell membrane can be rotated in real time.

Crash Simulations

Wire Frame Mapping

Force tube

Drawback Major draw back is the image quality. Usually for high quality images Ray Tracing is used.

References Alan Watt, 3D Computer graphics. Addison – Wesley Fredrick M Weinhaus, Venkat Devarajan,Texture mapping 3D models of real-world scenes.ACM computing survey, Volume James F. Blinn and Martin E. Newel,Texture and Reflection in computer generated images. ACM computing survey.

References (Contd..) TextureMapping.pdf ml