Week 5 - Friday What did we talk about last time? Euler angles - PowerPoint PPT Presentation

Week 5 - Friday

 What did we talk about last time?  Euler angles  Quaternions  Started vertex blending and morphing

 If we animate by moving rigid bodies around each other, joints won't look natural  To do so, we define bones and skin and have the rigid bone changes dictate blended changes in the skin

 The following equation shows the effect that each bone i (and its corresponding animation transform matrix B i ( t ) and bone to world transform matrix M i ) have on the p , the original location of a vertex − − n 1 n 1 ∑ ∑ − = = 1 u ( t ) w B ( t ) M p where w 1 i i i i = = i 0 i 0  Vertex blending is popular in part because it can be computed in hardware with the vertex shader

 Morphing is the technique for interpolating between two complete 3D models  It has two problems:  Vertex correspondence ▪ What if there is not a 1 to 1 correspondence between vertices?  Interpolation ▪ How do we combine the two models?

 We're going to ignore the correspondence problem (because it's really hard)  If there's a 1 to 1 correspondence, we use parameter s ∈ [0,1] to indicate where we are between the models and then find the new location m based on the two locations p 0 and p 1 = − + m ( 1 s ) p s p 0 1  Morph targets is another technique that adds in weighted poses to a neutral model

 Finally, we deal with the issue of projecting the points into view space  Since we only have a 2D screen, we need to map everything to x and y coordinates  Like other transforms, we can accomplish projection with a 4 x 4 matrix  Unlike affine transforms, projection transforms can affect the w components in homogeneous notation

 An orthographic projection maintains the property that parallel lines are still   1 0 0 0 parallel after projection    The most basic orthographic projection 0 1 0 0   = P 0 matrix simply removes all the z values   0 0 0 0  This projection is not ideal because z   values are lost  0 0 0 1   Things behind the camera are in front  z -buffer algorithms don't work

 To maintain relative depths and allow for clipping, we usually set up a canonical view volume based on ( l , r , b , t , n , f ) +   2 r l  These letters simply refer to the six − 0 0   − − bounding planes of the cube r l r l   +  Left 2 t b −   0 0  Right = − − P 0   t b t b  Bottom +  2 f n  − 0 0  Top   − − f n f n  Near    0 0 0 1   Far  Here is the (OpenGL) matrix that translates all points and scales them into the canonical view volume

 OpenGL normalizes to a canonical view volume from +   2 r l − [-1,1] in x , [-1,1] in y , and [- 0 0   − − r l r l   1,1] in z + 2 t b −   0 0  Just to be silly, MonoGame = − − P 0   t b t b normalizes to a canonical  1 n  − 0 0   − − view volume of [-1,1] in x , [- f n f n   1,1] in y , and [0,1] in z  0 0 0 1   Thus, its projection matrix is:

 A perspective projection does not preserve parallel lines  Lines that are farther from the camera will appear smaller  Thus, a view frustum must be normalized to a canonical view volume  Because points actually move (in x and y ) based on their z distance, there is a distorting term in the w row of the projection matrix

 Here is the MonoGame projection matrix  It is different from the OpenGL again because it only uses [0,1] for z +   2 n r l 0 0   − − r l r l   + 2 n t b   0 0 = − − P 0   t b t b −  f fn  − 0 0   − − f n f n   −  0 0 1 0 

 Light  Materials  Sensors

 Read Chapter 5 for Monday  Finish Project 1  Due tonight by 11:59 p.m.!  Keep working on Assignment 2  Due next Friday