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1、Camera Models and Color,Department of CS & E, East China University of Science & Technology,Content,Camera Models Color in Vision Color perception Color representations,Content,Camera Models Color in Vision Color perception Color representations,Rendering with Natural Light,Fiat Lux,Light Stage,Movi
2、ng the Camera or the World?,Two equivalent operations Initial OpenGL camera position is at origin, looking along -Z Now create a unit square parallel to camera at z = -10 If we put a z-translation matrix of 3 on stack, what happens? Camera moves to z = -3 Note OpenGL models viewing in left-hand coor
3、dinates Camera stays put, but square moves to -7 Image at camera is the same with both,A 3D Scene,Notice the presence of the camera the projection plane the world coordinate axesViewing transformations define how to acquire the image on the projection plane,Viewing Transformations,Goal: To create a
4、camera-centered viewCamera is at origin Camera is looking along negative z-axis Cameras up is aligned with y-axis (what does this mean?),2 Basic Steps,Step 1: Align the worlds coordinate frame with cameras by rotation,2 Basic Steps,Step 2: Translate to align world and camera origins,Creating Camera
5、Coordinate Space,Specify a point where the camera is located in world space, the eye point (View Reference Point = VRP) Specify a point in world space that we wish to become the center of view, the lookat point Specify a vector in world space that we wish to point up in camera image, the up vector (
6、VUP) Intuitive camera movement,Constructing Viewing Transformation, V,Create a vector l from eye-point to lookat-pointNormalize the vectorDesired rotation matrix should map this vector to 0, 0, -1T Why?,Constructing Viewing Transformation, V,Construct another important vector from the cross product
7、of the lookat-vector and the vup-vectorThis vector, when normalized, should align with 1, 0, 0T Why?,Constructing Viewing Transformation, V,One more vector to defineThis vector, when normalized, should align with 0, 1, 0T Now lets compose the results,Composing Matrices to Form V,We know the three wo
8、rld axis vectors (x, y, z) We know the three camera axis vectors (u, v, n) Viewing transformation, V, must convert from world to camera coordinate systems,Composing Matrices to Form V,Remember Each camera axis vector is unit length. Each camera axis vector is perpendicular to othersCamera matrix is
9、orthogonal and normalized OrthonormalTherefore, M-1 = MT,Composing Matrices to Form V,Therefore, rotation component of viewing transformation is just transpose of computed vectors,Composing Matrices to Form V,Translation component tooMultiply it through,Final Viewing Transformation, V,To transform v
10、ertices, use this matrix:And you get this:,Canonical View Volume,A standardized viewing volume representationParallel (Orthogonal) Perspective,1,-1,-1,Front Plane,Front Plane,Back Plane,Back Plane,x or y = +/- z,Why do we care?,Canonical View Volume Permits Standardization Clipping Easier to determi
11、ne if an arbitrary point is enclosed in volume Consider clipping to six arbitrary planes of a viewing volume versus canonical view volume Rendering Projection and rasterization algorithms can be reused,Projection Normalization,One additional step of standardization Convert perspective view volume to
12、 orthogonal view volume to further standardize camera representation Convert all projections into orthogonal projections by distorting points in three space (actually four space because we include homogeneous coordinate w) Distort objects using transformation matrix,Projection Normalization,Building
13、 a transformation matrix How do we build a matrix that Warps any view volume to canonical orthographic view volume Permits rendering with orthographic camera,All scenes rendered with orthographic camera,Projection Normalization - Ortho,Normalizing Orthographic Cameras Not all orthographic cameras de
14、fine viewing volumes of right size and location (canonical view volume) Transformation must map:,Projection Normalization - Ortho,Two steps Translate center to (0, 0, 0) Move x by (xmax + xmin) / 2 Scale volume to cube with sides = 2 Scale x by 2/(xmax xmin) Compose these transformation matrices Res
15、ulting matrix maps orthogonal volume to canonical,Projection Normalization - Persp,Perspective Normalization is Trickier,Perspective Normalization,Consider N=After multiplying: p = Np,Perspective Normalization,After dividing by w, p - p,Perspective Normalization,Quick Check,If x = z x = -1 If x = -z
16、 x = 1,Perspective Normalization,What about z? if z = zmaxif z = zminSolve for a and b such that zmin -1 and zmax 1 Resulting z is nonlinear, but preserves ordering of points If z1 z2 ,then z1 z2,Perspective Normalization,We did it. Using matrix N Perspective viewing frustum transformed to cube Orth
17、ographic rendering of cube produces same image as perspective rendering of original frustum,Color,Next topic: ColorTo understand how to make realistic images, we need a basic understanding of the physics and physiology of vision. Here we step away from the code and math for a bit to talk about basic principles.,
