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Java 3D generates viewing matrices in one of a few different ways, depending on whether the end user has a head-mounted or a room-mounted display environment and whether or not head tracking is enabled This section describes the computation for a non-head-tracked, room-mounted display a standard computer display Other environments are described in Appendix C, View Model Details In the absence of head tracking, the ViewPlatform s origin speci es the virtual eye s location and orientation within the virtual world However, the eye location provides only part of the information needed to render an image The renderer also needs a projection matrix In the default mode, Java 3D uses the projection policy, the speci ed eld-of-view information, and the front and back clipping distances to construct a viewing frustum
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Composing Model and Viewing Transformations
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Figure 8-4 shows a simple scene graph To draw the object labeled S, Java 3D internally constructs the appropriate model, view platform, eye, and projection matrices Conceptually, the model transformation for a particular object is computed by concatenating all the matrices in a direct path between the object and the VirtualUniverse The view matrix is then computed again, conceptually by concatenating all the matrices between the VirtualUniverse object and the
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Version 11 Alpha 01, February 27, 1998
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ViewPlatform attached to the current View object The eye and projection matrices are constructed from the View object and its associated component objects In our scene graph, what we would normally consider the model transformation would consist of the following three transformations: LT1T2 By multiplying LT1T2 by a vertex in the shape object, we would transform that vertex into the virtual universe s coordinate system What we would normally consider the view platform transformation would be (LTv1) 1 or Tv1 1L 1 This presents a problem since coordinates in the virtual universe are 256-bit xed-point values, which cannot be used to ef ciently represent transformed points Fortunately, however, there is a solution to this problem Composing the model and view platform transformations gives us Tv1 1L 1LT1T2 = Tv1 1IT1T2 = Tv1 1T1T2, the matrix that takes vertices in an object s local coordinate system and places them in the ViewPlatform s coordinate system Note that the high-resolution Locale transformations cancel each other out, which removes the need to actually transform points into high-resolution VirtualUniverse coordinates The general formula of the matrix that transforms object coordinates to ViewPlatform coordinates is Tvn 1 Tv2 1Tv1 1T1T2 Tm As was mentioned above, the View object contains the remainder of the view information, speci cally, the eye matrix, E, that takes points in the ViewPlatform s local coordinate system and translates them into the user s eye coordinate system, and the projection matrix, P, that projects objects in the eye s coordinate system into clipping coordinates The nal concatenation of matrices for rendering our shape object S on the speci ed Canvas3D is PETv1 1T1T2 In general this is PETvn 1 Tv2 1Tv1 1T1T2 Tm The details of how Java 3D constructs the matrices E and P in different end-user con gurations are described in Appendix C, View Model Details
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Java 3D supports multiple high-resolution Locales In some cases, these Locales are close enough to each other that they can see each other, meaning that objects can be rendered even though they are not in the same Locale as the ViewPlatform object that is attached to the View Java 3D automatically handles this case without the application having to do anything As in the previous example, where the ViewPlatform and the object being rendered are attached to the same Locale, Java 3D internally constructs the appropriate matrices for cases in which the ViewPlatform and the object being rendered are not attached to the same Locale Let s take two Locales, L1 and L2, with the View attached to a ViewPlatform in L1 According to our general formula, the modeling transformation the transformation that takes points in object coordinates and transforms them into VirtualUniverse coordinates is LT1T2 Tm In our speci c example, a point in Locale L2 would be transformed into VirtualUniverse coordinates by L2T1T2 Tm The view platform transformation would be (L1Tv1Tv1 Tvn) 1 or Tvn 1 Tv2 1Tv1 1L1 1 Composing these two matrices gives us Tvn 1 Tv2 1Tv1 1L1 1L2T1T2 Tm
Version 11 Alpha 01, February 27, 1998