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# File Documents/Further Study.xml

`             object. So be aware of that when doing searches). A character is made of a hierarchy of`
`             transformations; each transform is called a bone. Vertices are weighted to particular`
`             bones. Where it gets interesting is that vertices can have weights to multiple bones.`
`-            This means that the vertex's final position is determined by combining the transforms by`
`-            two (or more) matrices.</para>`
`+            This means that the vertex's final position is determined by a weighted combination of`
`+            two (or more) transforms.</para>`
`         <para>Vertex shaders generally do this by taking an array of matrices as a uniform block.`
`             Each matrix is a bone. Each vertex contains a <type>vec4</type> which contains up to 4`
`             indices in the bone matrix array, and another <type>vec4</type> that contains the weight`
`         <para>This process is made more complicated by normals and the tangent-space basis necessary`
`             for bump mapping. And it is complicated even further by a technique called dual`
`             quaternion skinning. This is done primarily to avoid issues with certain bones rotating`
`-            relative to one another. It prevents the wrist bone from pinching inwards when it spins`
`-            relative to the forearm.</para>`
`+            relative to one another. It prevents vertices from pinching inwards when the wrist bone`
`+            is rotated 180 degrees from the forearm.</para>`
`         <formalpara>`
`             <title>BRDFs</title>`
`             <para>The term Bidirectional Reflectance Distribution Function (<acronym>BRDF</acronym>)`
`                 which are specified relative to the surface normal. This last part makes the BRDF`
`                 independent of the surface normal, as it is an implicit parameter in the equation.`
`                 The output of the BRDF is the percentage of light from the light source that is`
`-                reflected along the view direction. Thus, the output of the BRDF is multipled into`
`+                reflected along the view direction. Thus, the output of the BRDF is multiples into`
`                 the incident light intensity to produce the output light intensity.</para>`
`         </formalpara>`
`         <para>By all rights, this sounds like a lighting equation. And it is. Indeed, every lighting`
`             equation in this book can be expressed in the form of a BRDF. One of the things that`
`-            make BRDFs as a class of equations interesting is that you can actually take a material`
`-            into a lab, perform a series of tests on it, and produce a BRDF table out of them. This`
`-            BRDF table, typically expressed as a texture, can then be used to reflect how a surface`
`-            in the real world actually behaves under lighting conditions. This can provide much more`
`-            accurate results than using models as we have done.</para>`
`+            make BRDFs as a class of equations interesting is that you can actually take a physical`
`+            object into a lab, perform a series of tests on it, and produce a BRDF table out of`
`+            them. This BRDF table, typically expressed as a texture, can then be directly used by a`
`+            shader to show how a surface in the real world actually behaves under lighting`
`+            conditions. This can provide much more accurate results than using models as we have`
`+            done.</para>`
`         <formalpara>`
`             <title>Scalable Alpha Testing</title>`
`             <para>We have seen how alpha-test works via <literal>discard</literal>: a fragment is`