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zfergus · Aug 30, 2015 · 58df911 · 58df911
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diff --git a/Algorithms/3D-picking.html b/Algorithms/3D-picking.html
@@ -0,0 +1,76 @@
+<html>
+<body>
+<br>
+<center>
+<b>3D Vertex Picking</b><br>
+Zachary Ferguson
+</center>
+<br><hr><br>
+Let E be the Eye world coordinates, C be the viewing direction where |C| is the 
+viewing distance, U be the up vector, and &#952 and &#966 are the view half 
+angles.<br>
+<br>
+Convert the point selected in Normalized Device Coordinates to world coordinates
+and use it to create a ray equation in 3D space.
+<br>
+<strong>Step 1:</strong> Compute the horizontal screen vector, H, at the point 
+E.
+<ol>
+	<li>
+		A = C <font face="arial">x</font> U, where A||H and starts at E.
+	</li>
+	<li>
+		H = (A*|C|*tan(&#952))/(|A|), rescale A to H.
+	</li>
+</ol>
+<strong>Step 2:</strong> Compute the vertical screen vector, V, at the point E.
+<ol>
+	<li>
+		B = A <font face="arial">x</font> C, where B||V and starts at E.
+	</li>
+	<li>
+		V = (B*|C|*tan(&#966))/(|B|), rescale B to V.
+	</li>
+</ol>
+<strong>Step 3:</strong> Compute the midpoint of the screen, M.
+<ol>
+	<li>
+		M = E + C.
+	</li>
+</ol>
+<strong>Step 4:</strong> Compute P, the point in world 2D coordinates that the 
+user points at, given the point in Normalized Device Coordinates, 
+(s<sub>x</sub>, s<sub>y</sub>), 
+where 0 &#8804 s<sub>x</sub> &#8804 1 and 0 &#8804 s<sub>y</sub> &#8804 1.
+<ol>
+	<li>
+		P = M + (2s<sub>x</sub>-1)*H + (2s<sub>y</sub>-1)*V.
+	</li>
+</ol>
+<strong>Step 5:</strong> Compute the ray equation, R.
+<ol>
+	<li>
+		R = E + (t*(P - E))/(|P-E|), where t is the independent variable.
+	</li>
+</ol>
+Check for the vertices that the ray passes through, within a radius of r from 
+the vertex.
+<br>
+<strong>Step 6:</strong> For each vertex, v, in the mesh, compute the distance 
+from v to the ray, R, computed in step 5. If the distance is less than or equal 
+to r, then select that vertex.
+<ol>
+	<li>
+		R<sub>01</sub> = R(1) - R(0), where R<sub>01</sub> is the direction
+		vector of the ray.
+	</li>
+	<li>
+		d = |(R<sub>01</sub> <font face="arial">x</font> (v - R(0)))|, where d 
+		is the distance from the point to the ray and R(0) is the rays origin.
+	</li>
+	<li>
+		If d &#8804 r, then select v.
+	</li>
+</ol>
+</body>
+</html>
diff --git a/Algorithms/3D-picking.txt b/Algorithms/3D-picking.txt
@@ -0,0 +1,45 @@
+3D Vertex Picking
+Zachary Ferguson
+
+Let E be the Eye world coordinates, C be the viewing direction where |C| is the 
+viewing distance, U be the up vector, and theta and phi are the view half 
+angles.
+
+Convert the point selected in Normalized Device Coordinates to world coordinates
+and use it to create a ray equation in 3D space.
+
+Step 1: Compute the horizontal screen vector, H, at the point E.
+
+	a. A = C x U, where A||H and starts at E.
+	b. H = (A*|C|*tan(theta))/(|A|), rescale A to H.
+
+Step 2: Compute the vertical screen vector, V, at the point E.
+
+	a. B = A x C, where B||V and starts at E.
+	b. V = (B*|C|*tan(phi))/(|B|), rescale B to V.
+
+Step 3: Compute the midpoint of the screen, M.
+
+	a. M = E + C.
+
+Step 4: Compute P, the point in world 2D coordinates that the user points at, 
+given the point in Normalized Device Coordinates, (s_x, s_y), where 
+0 <= s_x <= 1 and 0 <= s_y <= 1.
+
+	a. P = M + (2*s_x - 1) * H + (2*s_y - 1) * V.
+
+Step 5: Compute the ray equation, R.
+
+	a. R = E + (t*(P - E))/(|P-E|), where t is the independent variable.
+
+Check for the vertices that the ray passes through, within a radius of r from 
+the vertex.
+
+Step 6: For each vertex, v, in the mesh, compute the distance from v to the ray, 
+R, computed in step 5. If the distance is less than or equal to r, then select 
+that vertex.
+
+	a. R_01 = R(1) - R(0), where R_01 is the direction vector of the ray.
+	b. d = |(R_01 x (v - R(0)))|, where d is the distance from the point to the
+	   ray and R(0) is the rays origin.
+	c. If d <= r, then select v.
diff --git a/Algorithms/fractalize.html b/Algorithms/fractalize.html
@@ -0,0 +1,41 @@
+<html>
+<body>
+<br>
+<center>
+<b>Fractalized Mesh Algorithm</b><br>
+Zachary Ferguson
+</center>
+<br><hr><br>
+<strong>Step 1:</strong> Sub-divide the mesh to create new vertices between the 
+original ones.
+<ol>
+	<li>
+		Use the original mesh to create a new mesh.
+	</li>
+	<li>
+		Copy over the values of the original mesh.
+	</li>
+	<li>
+		Add new rows and cols between the original rows and cols while copying.
+		<br>
+		These new vertices' heights should be the average of the adjacent 
+		original vertices' heights.
+	</li>
+</ol>
+
+<strong>Step 2:</strong> Change the new vertices' height value to a value 
+specified by a random function. <br>
+The range of the random function is half the previous range that the fractalize
+function was called.
+<ol>
+	<li>
+		Iterate over the new vertices
+	</li>
+	<li>
+		Change their heights by the result of the random function.
+	</li>
+</ol>
+
+<strong>Step 3:</strong> Set the mesh to be drawn to the newly fractalized mesh.
+</body>
+</html>
diff --git a/Algorithms/fractalize.txt b/Algorithms/fractalize.txt
@@ -0,0 +1,14 @@
+Step 1: Sub-divide the mesh to create new vertices between the original ones.
+
+	a.Use the original mesh to create a new mesh.
+	b.Copy over the values of the original mesh.
+	c.Add new rows and cols between the original rows and cols while copying.
+
+Step 2: Change the new vertices' height value to a value specified by a random 
+function. The range of the random function is half the previous range that the 
+fractalize function was called.
+
+	a. Iterate over the new vertices
+	b. Set their height to be the result of the random function.
+
+Step 3: Set the mesh to be drawn to the newly fractalized mesh.
diff --git a/Algorithms/more_vertices.txt b/Algorithms/more_vertices.txt
@@ -0,0 +1,53 @@
+/* Copies this mesh into a larger mesh and fractalizes it with a */
+/* range of deltaH.                                              */
+Mesh* Mesh::fractalize(float deltaH) const
+{
+	/* Get the first and last vertex to calculate the width and depth. */
+	vec4 begin = this->getVertex(0,0);
+	vec4 end = this->getVertex(this->getRows() - 1, this->getCols() - 1);
+	/* Create a new larger mesh. */
+	Mesh* newMesh = new Mesh((this->getRows()*2)-2, (this->getCols()*2)-2,
+		end[0] - begin[0], end[2] - begin[2], this->color, 
+		this->snowCapHeight);
+
+	/* Copy over the original values of the Mesh to the new mesh's even */
+	/* indecies. Run time complexity of O((r*c)/4).                     */
+	for (unsigned int newRow = 0, originalRow = 0; newRow < newMesh->getRows();
+		 newRow+=2, originalRow++)
+	{
+		for (unsigned int newCol = 0, originalCol = 0; newCol < newMesh->
+			 getCols(); newCol+=2, originalCol++)
+		{
+			newMesh->setVertex(newRow, newCol, 
+				this->getVertex(originalRow, originalCol));
+		}
+	}
+
+	/* Create new vectors that are averages of the original mesh's vectors. */
+	/* Run time complexity of O((r*c)/4).                                   */
+	for (unsigned int r = 0; r < newMesh->getRows(); r+=2)
+	{
+		for (unsigned int c = 1; c < newMesh->getCols(); c+=2)
+		{
+			vec4 prev = newMesh->getVertex(r, c - 1);
+			vec4 next = newMesh->getVertex(r, c + 1);
+			newMesh->setVertex(r, c, vec4((prev[0]+next[0])/2.0f,
+				(prev[1]+next[1])/2.0f, (prev[2]+next[2])/2.0f, 1.0));
+		}
+	}
+
+	/* Create new rows that are average of the above and below column */ 
+	/* values. Run time complexity of O((r*c)/2).                     */
+	for (unsigned int r = 1; r < newMesh->getRows(); r+=2)
+	{
+		for (unsigned int c = 0; c < newMesh->getCols(); c++)
+		{
+			vec4 prev = newMesh->getVertex(r-1, c);
+			vec4 next = newMesh->getVertex(r+1, c);
+			newMesh->setVertex(r, c, vec4((prev[0]+next[0])/2.0f,
+				(prev[1]+next[1])/2.0f, (prev[2]+next[2])/2.0f, 1.0));
+		}
+	}
+
+	return newMesh;
+}
diff --git a/Algorithms/subdivision.html b/Algorithms/subdivision.html
@@ -0,0 +1,55 @@
+<html>
+<body>
+<br>
+<center>
+<b>Catmull-Clark Subdivision Algorithm</b><br>
+Zachary Ferguson
+</center>
+<br><hr><br>
+<strong>Step 1:</strong> For each face in the mesh, create a new vertex at the 
+center of the face.
+<ol>
+	<li>
+		Average the face vertices' x, y, and z values.
+	</li>
+	<li>
+		Create a new vertex with these x, y, and z (center vertex).
+	</li>
+</ol>
+
+<strong>Step 2:</strong> For each edge in the mesh, create a new edge midpoint 
+vertex that is the average of the adjacent edge vertices and the adjacent face 
+vertices.
+<ol>
+	<li>
+		Sum the two adjacent edge vertices and the two adjacent face vertices 
+		created in "Step 1".
+	</li>
+	<li>
+		Divide this sum by four to yield the new edge vertex.
+	</li>
+</ol>
+<strong>Step 3:</strong> Update the original vertices to be an weighted average 
+of the surrounding face centres, new edge midpoints, and vertex.
+<ol>
+	<li>
+		Sum all of the face vertices for the faces that the vertex is part of, 
+		then divide the sum by the number of edges connected to the vertex.
+	</li>
+	<li>
+		Sum all of the midpoints of the edges that the vertex is part of, then 
+		multiply the sum by two and divide by the number of edges connected to the
+		vertex.
+	</li>
+	<li>
+		Multiply the vertex that is being updated by the number of edges 
+		connected to the vertex minus three and then divide by the number of 
+		edges connected to the vertex.
+	</li>
+	<li>
+		Update the vertex being updated to be the sum of the results from 1, 2, 
+		and 3.
+	</li>
+</ol>
+</body>
+</html>
diff --git a/Algorithms/subdivision.txt b/Algorithms/subdivision.txt
@@ -0,0 +1,26 @@
+Step 1: For each face in the mesh, create a new vertex at the center of the 
+face.
+
+	a. Average the face vertices' x, y, and z values.
+	b. Create a new vertex with these x, y, and z (center vertex).
+
+Step 2: For each edge in the mesh, create a new edge midpoint vertex that is the
+average of the adjacent edge vertices and the adjacent face vertices.
+
+	a. Sum the two adjacent edge vertices and the two adjacent face vertices 
+	   created in "Step 1".
+	b. Divide this sum by four to yield the new edge vertex.
+
+Step 3: Update the original vertices to be an weighted average of the 
+surrounding face centres, new edge midpoints, and vertex.
+
+	a. Sum all of the face vertices for the faces that the vertex is part of, 
+	   then divide the sum by the number of edges connected to the vertex.
+	b. Sum all of the midpoints of the edges that the vertex is part of, then 
+	   multiply the sum by 2 and divide by the number of edges connected to the 
+	   vertex.
+	c. Multiply the vertex that is being updated by (the number of edges 
+	   connected to the vertex - 3) and then divide by the  number of edges 
+	   connected to the vertex.
+	d. Update the vertex being updated to be the sum of the results from a, b, 
+	   and c.
diff --git a/CS351_FP_FERGUSON.sln b/CS351_FP_FERGUSON.sln
@@ -0,0 +1,22 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio 2013
+VisualStudioVersion = 12.0.30501.0
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "CS351_FP_FERGUSON", "CS351_FP_FERGUSON.vcxproj", "{5F5D63DB-5BC0-4F1F-8861-D407A15420BC}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Win32 = Debug|Win32
+		Release|Win32 = Release|Win32
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{5F5D63DB-5BC0-4F1F-8861-D407A15420BC}.Debug|Win32.ActiveCfg = Debug|Win32
+		{5F5D63DB-5BC0-4F1F-8861-D407A15420BC}.Debug|Win32.Build.0 = Debug|Win32
+		{5F5D63DB-5BC0-4F1F-8861-D407A15420BC}.Release|Win32.ActiveCfg = Release|Win32
+		{5F5D63DB-5BC0-4F1F-8861-D407A15420BC}.Release|Win32.Build.0 = Release|Win32
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+EndGlobal