Homogeneous Coordinate - Interactive 3D Graphics

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The four values produced are X, Y, Z and W. These are called homogeneous
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coordinates and they're used for projection. What we do next with these
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coordinate values is divide each value by the W of the coordinate. This is
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called the prospective divide or homogeneous divide. So for our three test
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points we had a value such as 0, 0, negative 1, 1. Dividing by 1 is simple
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enough. That gives us 0, 0, negative 1. We don't need to bother writing out the
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W value in the results, since W divided by W will always equal 1. For our next
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point, W is 11. Dividing all these coordinates by 11 gives 0, 1, 1. Our last
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point is a little more interesting. Dividing through by W gives us 0, 0.67,
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0.83. Here are plots of the original points and view space and their
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corresponding new locations. Notice that the negative Z axis is pointing to the
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right for the frustum, and the resulting axis is plus Z to the right. Look at
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what's happened with these points and where they're transformed. They started
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inside or on the edge of our frustum. After the projection matrix is applied
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and division by W is performed the resulting points are in normalized device
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coordinates, anything in the range negative 1 to 1 for X, Y and Z is in the
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visible view volume. Let's take another example to show what happens to three
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objects that are the same size in world space but at different distances. When
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we transform to normalized device coordinates the relative area of coverage of
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the near plane stays the same. That is, the close object was half as high as
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the screen in our frustum view and transforms to half the height in NDC space.
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The second object is farther away and shows up as smaller. The third object on
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the back of the frustum is indeed much smaller than the others in normalized
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device coordinates. You might have noticed an interesting thing has happened to
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the depth of the second object. It started in the middle but it's moved
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backwards. We'll talk more about that in a bit as it's important.
Title:
Homogeneous Coordinate - Interactive 3D Graphics
Video Language:
English
Team:
Udacity
Project:
CS291 - Intro to 3D Computer Graphics
Duration:
01:48
 Udacity Robot edited English subtitles for Homogeneous Coordinate - Interactive 3D Graphics Cogi-Admin added a translation

English subtitles

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