Transformations & Transformations & Coordinate Systems - - PowerPoint PPT Presentation

Slide 1 CSCD 472? 4/5/10

Transformations & Coordinate Systems Transformations & Coordinate Systems

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Transformations: Basic Definitions Transformations: Basic Definitions

Basic definitions

Coordinate systems in RenderMan are always LEFT handed with the positive z-axis pointing into the screen (in world coordinates) The fixed or default camera is located at the

• rigin and points down the positive z-axis

All transformations are represented as 4 X 4 transformation matrices. Points are transformed by post-multiplication and matrices are concatenated using pre- multiplication (before concatenation) The matrix on top of the transformation stack is called the “current transformation matrix”. It is also said to represent “local coordinates”

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Transformation Commands Transformation Commands

Transformation Commands

each pre-multiplies (before concatenates current transform matrix with no preceeding push. Translate dx dy dz Rotate angle vx vy vz rotations are always counter-clockwise around the axis given Skew angle vx vy vz ax ay az angles are given in degrees Shearing transform – moves everything along a vector parallel to A = (ax, ay, az) – amount of shift depends on distance of vertex V=(vx,vy,vz) from plane defined by A and A X V

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Transformation Commands Transformation Commands

Transformation Commands

ConcatTransform matrix pre-concatenates the current matrix with matrix – often used to setup a gluLookAt style of camera transorm. Identity replaces current matrix with an identity matrix – In a world block returns the local coordinate system to be equal to the world coordinate system. Transform matrix replaces current matrix with the provided matrix – equivalent to Identity followed by ConcatTransform matrix.

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Saving and Restoring the Current Transformation Matrix Saving and Restoring the Current Transformation Matrix

Effects of blocks on Current Transformation Matrix (CTM)

AttributeBegin – starts an attribute block automatically pushes current attributes and CTM – the CTM does NOT change. AttributeEnd – pops most previous attributes and replaces CTM with one on the top of the stack. TransformBegin – pushes only the CTM but not the attributes – allows change of movement w/o affecting the attributes. TransformEnd – pops most previous CTM only.

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Special Coordinate Systems Special Coordinate Systems

“camera” Space

exists around the virtual camera – camera is at the origin of a left-handed coordinate system looking down positive z-axis forms the center of the visual universe – other coordinate systems emanate from this one. Cameras are not objects. Created when Projection is called sets the current transformation matrix to identity – all transformations that occur from here to the WorldBegin call build up the “world- to-camera” matrix. At WorldBegin the current transformation matrix is stored as the final “world-to-camera” matrix and the current transformation matrix is reset to identity.

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Special Coordinate Systems Special Coordinate Systems

“camera” Space

As in OpenGL this is the coordinate system in which all transforms have been applied including the “camera” transform. We (OpenGL orientation) visualize the camera transform as moving objects in world space so their position relative to the fixed camera is what it would have been with respect to the virtual camera. RenderMan prefers us to visualize the camera transform as a transformation of the camera coordinate system to produce world coordinates. Both views produce the same result – in OpenGL we start with one universal coordinate system and move

• bjects to where we want them (backwards) – in

RenderMan we transform one coordinate system into another (forwards).

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Special Coordinate Systems Special Coordinate Systems

“world” Space

initialized at WorldBegin relative to camera space from WorldBegin to WorldEnd changes to the current transformation matrix create new “local coordinate systems” that are relative to “world” space. This matrix transforms points from the “local” coordinate system into world space. In OpenGL – we build most objects relative to the universal coordinate system – often around the origin

• and then move them to where we want them – we

call this a “modeling” transform. In RenderMan we go the other direction and transform world coordinates to “object” or “local” coordinates and produce the same final result.

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Special Coordinate Systems Special Coordinate Systems

“object” (“local”) Space

These concepts need to be described carefully – Advanced RenderMan uses this explanation of local coordinate: When primitives are created, they take their positions from the current transformation matrix at the time and that becomes the “object” space for that particular object. Depending on the interpretation of the pronoun “that” this passage seems to imply that “object” and “local” space are the same as “world” space. The transform that takes “world” coordinates to “object” coordinates is actually the modeling transform considered from the “forward” rather than “backward” point of view.

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Special Coordinate Systems Special Coordinate Systems

“shader” Space

When shaders are created (with Surface or other calls) the “local” or “object” coordinate system is stored as the “shader space” for that particular shader. Since in “object” coordinates the center of the object is the origin of the coordinate system, shaders work with respect to the object itself without any regard to the transforms that are applied to the object.

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RIB File Illustrating Coordinate Spaces RIB File Illustrating Coordinate Spaces

Display "Transforms" "framebuffer" "rgba" . . . . Projection "perspective" "fov" 45 Translate 0 0 5 Rotate -50 1 0 0 Rotate 20 0 1 0 WorldBegin ## begining of the workd blockWorldBegin AttributeBegin Color [0.9 0.4 0.1] Rotate -90 1 0 0 Translate 1 0 0 Cone [1.0 0.5 360] AttributeEnd WorldEnd

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Rendering with defaultsurface Rendering with defaultsurface

Rendered with defaultlight and defaultsurface shaders

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Special Coordinate Systems Special Coordinate Systems

“screen” Space

projected 2D coordinates – x is right and y is up z coords mapped to 0 – 1

“NDC” coordinates

Normalized Device Coordinates – upper left is (0, 0) lower-right is (1.0, 1.0) CropWindow defined in this space

“raster” coordinates

resolution dependent 2D pixel coordinates upper- left is (0, 0) lower-right is (xres, yres) pixel addresses

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Coordinate System Commands Coordinate System Commands

CoordinateSystem name

names the current local coordinate system with name for later reference

CoordSysTransform name

replaces the current matrix with the one that forms the name coordinate – used to add

• bjects directly into that local coordinate

space.