Modeling Transform vs. Viewing Transform in 3D
Transforms: |
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As Modeling Transform: |
As Viewing Transform: |
Transforms: |
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As Modeling Transform: |
As Viewing Transform: |
The point of this demo is to help you to understand the equivalence between modeling transformations and viewing transformations in 3D. Modeling transforms apply to objects; they scale, rotate, and translate objects. A viewing transform can scale, rotate and translate the viewer. (This demo, however, only does translation and rotation, not scaling.)
In OpenGL, if we keep the same projection, so that the size and shape of the view volume remains unchanged, then we can think of the viewing transform as moving the view volume around in 3D space. As the viewer moves, the region in space enclosed by the view volume will change.
The image in the top left section of the demo shows a view of a 3D scene consisting of eight cubes. The projection is a perspective projection, with the viewer fairly close to the cubes. The sliders to the right allow you to control the modelview transformation that is used to create image. But are they applied to the objects as modeling transforms, or are they applied to the viewer?
The two lower pictures will help you understand that the question can't really be answered, because of the equivalence between the two types of transformation. They give a bird's eye view of the scene, from a different perspective. The view volume for the upper left image is shown as a translucent gray box in the lower images. Remember that the view volume encloses the region in 3D space that is rendered in the upper image. Note that in the initial configuration, sections of the four back cubes lie outside the view volume and so are not visible in the image.
Suppose that you apply transforms by dragging the sliders. In the image on the lower left, the view volume remains fixed, while the objects move around. This is visualizing the transforms as a modeling transformation. At the same time, in the image in the lower right, the objects remain fixed, while the viewport moves around. This is visualizing the same transforms as a viewing transformation.
You should notice that in both pictures, the contents of the view volume are exactly the same, and they agree with what is rendered in the image.
Spend some time playing with the sliders! Try dragging the z-translation slider back and forth, and notice how different parts of the cubes are cut off as they move into and out of the view volume. Notice how the effect of a transform on the objects is the opposite of its effect on the view volume. It will be easiest to see what is going on if you work with one slider at a time. Use the "Reset" button to reset all the sliders to their initial values.
