tweaks to matrix decomposition wording

Author: cmarrin

css3-2d-transforms/Overview.html

@@ -681,7 +681,7 @@ <h3 id=unmatrix><span class=secno>7.2. </span>Unmatrix</h3>
   <pre>
   Input:  matrix      ; a 4x4 matrix
   Output: translate   ; a 3 component vector
-          rotate      ; euler angles, represented as a 3 component vector
+          rotate      ; Euler angles, represented as a 3 component vector
           scale       ; a 3 component vector
           skew        ; skew factors XY,XZ,YZ represented as a 3 component vector
           perspective ; a 4 component vector
@@ -713,15 +713,15 @@ <h3 id=unmatrix><span class=secno>7.2. </span>Unmatrix</h3>
   if (matrix[3][3] == 0)
       return false
 
-  for (i = 0; i < 4; i++)
-      for (j = 0; j < 4; j++)
+  for (i = 0; i &lt; 4; i++)
+      for (j = 0; j &lt; 4; j++)
           matrix[i][j] /= matrix[3][3]
 
   // perspectiveMatrix is used to solve for perspective, but it also provides
   // an easy way to test for singularity of the upper 3x3 component.
   perspectiveMatrix = matrix
 
-  for (i = 0; i < 3; i++)
+  for (i = 0; i &lt; 3; i++)
       perspectiveMatrix[i][3] = 0
 
   perspectiveMatrix[3][3] = 1
@@ -760,7 +760,7 @@ <h3 id=unmatrix><span class=secno>7.2. </span>Unmatrix</h3>
   matrix[3][2] = 0
 
   // Now get scale and shear. 'row' is a 3 element array of 3 component vectors
-  for (i = 0; i < 3; i++)
+  for (i = 0; i &lt; 3; i++)
       row[i][0] = matrix[i][0]
       row[i][1] = matrix[i][1]
       row[i][2] = matrix[i][2]
@@ -778,7 +778,7 @@ <h3 id=unmatrix><span class=secno>7.2. </span>Unmatrix</h3>
   row[1] = normalize(row[1])
   skew[0] /= scale[1];
 
-  // Compute XZ and YZ shears, orthogonalize 3rd row
+  // Compute XZ and YZ shears, make 3rd row orthogonal
   skew[1] = dot(row[0], row[2])
   row[2] = combine(row[2], row[0], 1.0, -skew[1])
   skew[2] = dot(row[1], row[2])
@@ -794,8 +794,8 @@ <h3 id=unmatrix><span class=secno>7.2. </span>Unmatrix</h3>
   // Check for a coordinate system flip.  If the determinant
   // is -1, then negate the matrix and the scaling factors.
   pdum3 = cross(row[1], row[2])
-  if (dot(row[0], pdum3) < 0)
-      for (i = 0; i < 3; i++) {
+  if (dot(row[0], pdum3) &lt; 0)
+      for (i = 0; i &lt; 3; i++) {
           scale[0] *= -1;
           row[i][0] *= -1
           row[i][1] *= -1
@@ -818,9 +818,8 @@ <h3 id=animating-the-components><span class=secno>7.3. </span>Animating the
   <p> Once decomposed, each component of each returned value of the source
    matrix is linearly interpolated with the corresponding component of the
    destination matrix. For instance, the translate[0], translate[1] and
-   translate[2] values are interpolated as any other numeric value (see CSS3
-   Animations spec), and the result is used to set the translation of the
-   animating element.
+   translate[2] values are interpolated numerically, and the result is used
+   to set the translation of the animating element.
 
   <h3 id=recomposing-the-matrix><span class=secno>7.4. </span>Recomposing the
    matrix</h3>

css3-2d-transforms/Overview.src.html

@@ -627,7 +627,7 @@ <h3 id="unmatrix">Unmatrix</h3>
       <pre>
   Input:  matrix      ; a 4x4 matrix
   Output: translate   ; a 3 component vector
-          rotate      ; euler angles, represented as a 3 component vector
+          rotate      ; Euler angles, represented as a 3 component vector
           scale       ; a 3 component vector
           skew        ; skew factors XY,XZ,YZ represented as a 3 component vector
           perspective ; a 4 component vector
@@ -659,15 +659,15 @@ <h3 id="unmatrix">Unmatrix</h3>
   if (matrix[3][3] == 0)
       return false
 
-  for (i = 0; i < 4; i++)
-      for (j = 0; j < 4; j++)
+  for (i = 0; i &lt; 4; i++)
+      for (j = 0; j &lt; 4; j++)
           matrix[i][j] /= matrix[3][3]
 
   // perspectiveMatrix is used to solve for perspective, but it also provides
   // an easy way to test for singularity of the upper 3x3 component.
   perspectiveMatrix = matrix
 
-  for (i = 0; i < 3; i++)
+  for (i = 0; i &lt; 3; i++)
       perspectiveMatrix[i][3] = 0
 
   perspectiveMatrix[3][3] = 1
@@ -706,7 +706,7 @@ <h3 id="unmatrix">Unmatrix</h3>
   matrix[3][2] = 0
 
   // Now get scale and shear. 'row' is a 3 element array of 3 component vectors
-  for (i = 0; i < 3; i++)
+  for (i = 0; i &lt; 3; i++)
       row[i][0] = matrix[i][0]
       row[i][1] = matrix[i][1]
       row[i][2] = matrix[i][2]
@@ -724,7 +724,7 @@ <h3 id="unmatrix">Unmatrix</h3>
   row[1] = normalize(row[1])
   skew[0] /= scale[1];
 
-  // Compute XZ and YZ shears, orthogonalize 3rd row
+  // Compute XZ and YZ shears, make 3rd row orthogonal
   skew[1] = dot(row[0], row[2])
   row[2] = combine(row[2], row[0], 1.0, -skew[1])
   skew[2] = dot(row[1], row[2])
@@ -740,8 +740,8 @@ <h3 id="unmatrix">Unmatrix</h3>
   // Check for a coordinate system flip.  If the determinant
   // is -1, then negate the matrix and the scaling factors.
   pdum3 = cross(row[1], row[2])
-  if (dot(row[0], pdum3) < 0)
-      for (i = 0; i < 3; i++) {
+  if (dot(row[0], pdum3) &lt; 0)
+      for (i = 0; i &lt; 3; i++) {
           scale[0] *= -1;
           row[i][0] *= -1
           row[i][1] *= -1
@@ -762,8 +762,8 @@ <h3>Animating the components</h3>
       <p>
           Once decomposed, each component of each returned value of the source matrix is linearly interpolated 
           with the corresponding component of the destination matrix. For instance, the translate[0], 
-          translate[1] and translate[2] values are interpolated as any other numeric value (see CSS3 
-          Animations spec), and the result is used to set the translation of the animating element. 
+          translate[1] and translate[2] values are interpolated numerically, and the result is used to set the 
+          translation of the animating element. 
       </p>
       <h3>Recomposing the matrix</h3>
       <p><em>This section is not normative.</em></p>