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Jason McKesson committed 2a0bec0

Added equations to tuts 0, 8, 9, and 10.
Other Misc editing.

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File Documents/Basics/ColumnVector.mathml

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File Documents/Basics/ColumnVector.svg

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File Documents/Basics/Tutorial 00.xml

         <para>When writing vectors in text, they are written with parenthesis. So a 3D vector could
             be (0, 2, 4); the X component is 0, the Y component is 2, and the Z component is 4. When
             writing them as part of an equation, they are written as follows:</para>
-        <!--TODO: Show a column vector.-->
-        <para>In math equations, vector variables are either bold or written with an arrow over
-            them.</para>
+        <informalequation>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="ColumnVector.svg"/>
+                </imageobject>
+            </mediaobject>
+        </informalequation>
+        <para>In math equations, vector variables are either in boldface or written with an arrow
+            over them.</para>
         <para>When drawing vectors graphically, one makes a distinction between position vectors and
             direction vectors. However, numerically there is <emphasis>no</emphasis> difference
             between the two. The only difference is in how you use them, not how you represent them
             <!--TODO: Show A+B again, with B moved to the tip of A.-->
             <para>Numerically, the sum of two vectors is just the sum of the corresponding
                 components:</para>
-            <!--TODO: Show vector addition in equation form.-->
+        <equation>
+            <title>Vector Addition with Numbers</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorAdditionNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
             <para>Any operation where you perform an operation on each component of a vector is
                 called a <glossterm>component-wise operation</glossterm>. Vector addition is
                 component-wise. Any component-wise operation on two vectors requires that the two
         </formalpara>
         <!--TODO: Show vectors A and -A.-->
             <para>Numerically, this means negating each component of the vector.</para>
-            <!--TODO: Show negation in equation form.-->
-            <para>Just as with regular math, vector subtraction is the same as addition with the
-                negation of the second vector.</para>
+        <equation>
+            <title>Vector Negation</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorNegationNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
+            <para>Just as with scalar math, vector subtraction is the same as addition with the
+            negation of the second vector.</para>
             <!--TODO: Geometrically show vector subtraction.-->
         <formalpara>
             <title>Vector Multiplication</title>
-            <para>Vector multiplication is one of the few vector operations that has no geometric
-                equivalent. Multiplying two vectors numerically is simply component-wise
-                multiplication, much like vector addition.</para>
+            <para>Vector multiplication is one of the few vector operations that has no real
+                geometric equivalent. To multiply a direction by another, or multiplying a position
+                by another position, doesn't really make sense. That doesn't mean that the numerical
+                equivalent isn't useful, though.</para>
         </formalpara>
-        <!--TODO: Numerically show vector multiplication.-->
+        <para>Multiplying two vectors numerically is simply component-wise multiplication, much like
+            vector addition.</para>
+        <equation>
+            <title>Vector Multiplication</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorMultiplicationNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
         <formalpara>
             <title>Vector/Scalar Operations</title>
             <para>Vectors can be operated on by scalar values. Recall that scalars are just single
         <!--TODO: Graph of a vector, that vector times 3, and that vector times 0.5.-->
         <para>Numerically, this is a component-wise multiplication, where each component of the
             vector is multiplied with each component of the scalar.</para>
-        <!--TODO: Equation of vector-scalar multiplication.-->
-        <para>Scalars can also be added to scalars. This, like vector-to-vector multiplication, has
+        <equation>
+            <title>Vector-Scalar Multiplication</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorScalarMultNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
+        <para>Scalars can also be added to vectors. This, like vector-to-vector multiplication, has
             no geometric representation. It is a component-wise addition of the scalar with each
             component of the vector.</para>
-        <!--TODO: Equation of vector-scalar addition.-->
+        <equation>
+            <title>Vector-Scalar Addition</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorScalarAddNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
         <formalpara>
             <title>Vector Algebra</title>
             <para>It is useful to know a bit about the relationships between these kinds of vector
                 operations.</para>
         </formalpara>
-        <para>Vector addition and multiplication follow the same rules for scalar addition and
-            multiplication. They are commutative, associative, and distributive.</para>
-        <!--TODO: Equation for commutative, associative, and distributive vector math.-->
-        <para>Scalar operations have similar properties.</para>
+        <para>Vector addition and multiplication follow many of the same rules for scalar addition
+            and multiplication. They are commutative, associative, and distributive.</para>
+        <equation>
+            <title>Vector Algebra</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorMathProperties.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
+        <para>Vector/scalar operations have similar properties.</para>
         <formalpara>
             <title>Length</title>
             <para>Vectors have a length. The length of a vector is the distance from the starting
         </formalpara>
         <!--TODO: Show a graph of a vector and its length.-->
         <para>Numerically, computing the distance requires this equation:</para>
-        <!--TODO: Equation for distance computation.-->
+        <equation>
+            <title>Vector Length</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorLengthNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
         <formalpara>
             <title>Unit Vectors and Normalization</title>
             <para>A vector that has a length of exactly one is called a <glossterm>unit
         <para>A vector can be converted into a unit vector by <glossterm>normalizing</glossterm> it.
             This is done by dividing the vector by its length. Or rather, multiplication by the
             reciprocal of the length.</para>
-        <!--TODO: Equation for normalization of a vector.-->
+        <equation>
+            <title>Vector Normalization</title>
+            <mediaobject>
+                <imageobject>
+                    <imagedata format="SVG" fileref="VectorNormalizationNum.svg"/>
+                </imageobject>
+            </mediaobject>
+        </equation>
         <para>This is not all of the vector math that we will use in these tutorials. New vector
             math operations will be introduced and explained as needed when they are first used. And
             unlike the math operations introduced here, most of them are not component-wise

File Documents/Basics/Tutorial 01.xml

                 position, this shader simply copies it directly into the output.</para>
             <formalpara>
                 <title>Vertex Attributes</title>
+                <para>Shaders have inputs and outputs. Think of these like function parameters and
+                    function return values. If the shader is a function, then it is called with
+                    input values, and it is expected to return a number of output values.</para>
             </formalpara>
-            <para>Shaders have inputs and outputs. Think of these like function parameters and
-                function return values. If the shader is a function, then it is called with input
-                values, and it is expected to return a number of output values.</para>
             <para>Inputs to and outputs from a shader stage come from somewhere and go to somewhere.
                 Thus, the input <varname>position</varname> in the vertex shader must be filled in
                 with data somewhere. So where does that data come from? Inputs to a vertex shader

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