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Tot08: Round Gimbals.

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# File Documents/Positioning/Tutorial 07.xml

`                 the target moves, the camera will follow it perfectly.</para>`
`             <para>To do this, we use a special coordinate system trick. Instead of storing the`
`                 relative position of the camera in a normal coordinate system, we instead use a`
`-                    <glossterm>spherical coordinate system.</glossterm></para>`
`+                    <glossterm>spherical coordinate system</glossterm>, also known as`
`+                    <glossterm>polar coordinates</glossterm>.</para>`
`             <para>Previously, we said that a coordinate system was defined by a series of vectors`
`                 and an origin point. This was a useful simplification of the possibilities; this is`
`                 true of any coordinate system that follows the rules of <glossterm>Euclidean`
`                 </glossdef>`
`             </glossentry>`
`             <glossentry>`
`-                <glossterm>spherical coordinate system</glossterm>`
`+                <glossterm>spherical coordinate system, polar coordinates</glossterm>`
`                 <glossdef>`
`                     <para>A three dimensional coordinate system where the three coordinates are not`
`                         defined by 3 values multiplied by vectors, but by two angles and a radius.`

# File Documents/Positioning/Tutorial 08.xml

`     <section>`
`         <?dbhtml filename="Tut08 Gimbal Lock.html"?>`
`         <title>Gimbal Lock</title>`
`-        <para>Remember back when we said that n rotation matrix isn't a rotation matrix at all, that`
`-            it is an orientation matrix? We also said that forgetting this can come back to bite`
`-            you. Well, here's likely the most common way.</para>`
`+        <para>Remember a few tutorials back, when we said that a rotation matrix isn't a rotation`
`+            matrix at all, that it is an orientation matrix? We also said that forgetting this can`
`+            come back to bite you. Well, here's likely the most common way.</para>`
`         <para>Normally, when dealing with orienting an object like a plane or spaceship in 3D space,`
`             you want to orient it based on 3 rotations about the 3 axes. The obvious way to do this`
`             is with a series of 3 rotations. This means that the program stores 3 angles, and you`
`         <para>When gimbals are in such a position, you have what is known as <glossterm>gimbal`
`                 lock</glossterm>; you have locked one of the gimbals to another, and now both cause`
`             the same effect.</para>`
`-        <para>How do you fix this problem? There are several possible solutions to the`
`-            problem.</para>`
`-        <para>Perhaps the most optimal solution is to simply not use gimbals. After all, if you`
`-            don't have gimbals, you can't gimbal lock. Instead of storing the orientation as a`
`-            series of rotations, store the orientation as an <emphasis>orientation.</emphasis> That`
`-            is, maintain the current orientation as a matrix. When you need to modify the`
`-            orientation, you apply a transformation to this matrix, storing the result as the new`
`-            current orientation.</para>`
`-        <para>This means that every yaw, pitch, and roll applied to the current orientation will be`
`-            relative to that current orientation. Which is usually exactly what you want. If the`
`-            user applies a positive yaw, you want that yaw to rotate them relative to where they are`
`-            current pointing.</para>`
`-        <para>A downside of this approach, besides the size penalty of having to store a 4x4 matrix`
`-            rather than 3 floating-point angles, is that floating-point math can lead to errors. If`
`-            you keep accumulating successive transformations of an object, once every 1/30th of a`
`-            second for a period of several minutes or hours, these floating-point errors start`
`-            accumulating. Eventually, the orientation stops being a pure rotation and starts`
`-            incorporating scale and skewing characteristics.</para>`
`-        <para>The solution here is to re-orthonormalize the matrix after applying each transform. A`
`-            transform (space) is said to be <glossterm>orthonormal</glossterm> if the basis vectors`
`-            are of unit length (no scale) and each axis is perpendicular to all of the`
`-            others.</para>`
`-        <para>Unfortunately, re-orthonormalizing a matrix is not a simple operation. You could try`
`-            to normalize each of the axis vectors with typical vector normalization, but that`
`-            wouldn't ensure that the matrix was orthonormal. It would remove scaling, but the axes`
`-            wouldn't be guaranteed to be perpendicular.</para>`
`-        <para>The proper solution is to use <link`
`-                xlink:href="http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation">unit`
`-                quaternions</link> to store orientations, which can be orthonormalized much more`
`-            easily. This is beyond the scope of this tutorial, but the Wikipedia article on the`
`-            subject is a good place to start.</para>`
`         <section>`
`             <title>Complex Mesh Space</title>`
`             <para>The way this tutorial renders each gimbal serves as an object lesson in the use of`
`     </section>`
`     <section>`
`         <title>Quaternions</title>`
`-        <para/>`
`+        <para>How do you fix this problem? There are several possible solutions to the`
`+            problem.</para>`
`+        <para>Perhaps the most optimal solution is to simply not use gimbals. After all, if you`
`+            don't have gimbals, you can't gimbal lock. Instead of storing the orientation as a`
`+            series of rotations, store the orientation as an <emphasis>orientation.</emphasis> That`
`+            is, maintain the current orientation as a matrix. When you need to modify the`
`+            orientation, you apply a transformation to this matrix, storing the result as the new`
`+            current orientation.</para>`
`+        <para>This means that every yaw, pitch, and roll applied to the current orientation will be`
`+            relative to that current orientation. Which is usually exactly what you want. If the`
`+            user applies a positive yaw, you want that yaw to rotate them relative to where they are`
`+            current pointing.</para>`
`+        <para>A downside of this approach, besides the size penalty of having to store a 4x4 matrix`
`+            rather than 3 floating-point angles, is that floating-point math can lead to errors. If`
`+            you keep accumulating successive transformations of an object, once every 1/30th of a`
`+            second for a period of several minutes or hours, these floating-point errors start`
`+            accumulating. Eventually, the orientation stops being a pure rotation and starts`
`+            incorporating scale and skewing characteristics.</para>`
`+        <para>The solution here is to re-orthonormalize the matrix after applying each transform. A`
`+            transform (space) is said to be <glossterm>orthonormal</glossterm> if the basis vectors`
`+            are of unit length (no scale) and each axis is perpendicular to all of the`
`+            others.</para>`
`+        <para>Unfortunately, re-orthonormalizing a matrix is not a simple operation. You could try`
`+            to normalize each of the axis vectors with typical vector normalization, but that`
`+            wouldn't ensure that the matrix was orthonormal. It would remove scaling, but the axes`
`+            wouldn't be guaranteed to be perpendicular.</para>`
`+        <para>So instead, we need to use a different way of storing an orientation. To do this, we`
`+            use something called a <glossterm>quaternion.</glossterm></para>`
`+        <para>A quaternion is (for the purposes of this conversation) a 4-dimensional vector that is`
`+            treated in a special way. Any change of orientation from one coordinate system to`
`+            another can be represented by a rotation about some axis by some angle. A quaternion is`
`+            a way of encoding this angle/axis rotation:</para>`
`+        <!--TODO: Equation: build XYZW of a quaternion from an angle/axis rotation.-->`
`+        <para>This will produce a <glossterm>unit quaternion.</glossterm> That is, a quaternion with`
`+            a length of 1.</para>`
`+        <section>`
`+            <title>Quaternion Math</title>`
`+            <para>Quaternions are equivalent to orientation matrices. You can compose two`
`+                orientation quaternions using a special operation called <glossterm>quaternion`
`+                    multiplication</glossterm>.</para>`
`+            <!--TODO: Equation: two quaternions and the multiplication of them.-->`
`+            <para>If the two quaternions being multiplied represent orientations, then the product`
`+                of them is a composite orientation. Just as with matrix multiplication, only`
`+                specifically for orientations. Like matrix multiplication, quaternion multiplication`
`+                is associative (<informalequation>`
`+                    <mathphrase>(a*b) * c = a * (b*c)</mathphrase>`
`+                </informalequation>), but not commutative (<informalequation>`
`+                    <mathphrase>a*b != b*a</mathphrase>`
`+                </informalequation>).</para>`
`+            <para>The main difference that helps us solve the Gimbal lock problem is that it is easy`
`+                to keep a quaternion normalized. Simply perform a vector normalization on it after`
`+                every few multiplications. This enables us to add numerous small rotations together`
`+                without numerical precision problems showing up.</para>`
`+            <para>There is one more thing we need to be able to do: convert a quaternion into a`
`+                rotation matrix. While we could convert a unit quaternion back into angle/axis`
`+                rotations, it's much preferable to do it directly:</para>`
`+            <!--TODO: Equation: compute rotation matrix from a quaternion.-->`
`+        </section>`
`+        <section>`
`+            <title>Composition Type</title>`
`+            <para>So our goal is to compose successive rotations into a final orientation. When we`
`+                want to increase the pitch, for example, we will take the current orientation and`
`+                multiply into it a quaternion that represents a pitch rotation of a few degrees. The`
`+                result becomes the new orientation.</para>`
`+            <para>But which side do we do the multiplication on? Quaternion multiplication is not`
`+                commutative, so this will have an affect on the output. Well, it works exactly like`
`+                matrix math.</para>`
`+            <para>If you multiply the pitch increase on the left side, then it changes the pitch`
`+                relative to the current orientation. If you multiply the pitch on the right side, it`
`+                changes the pitch relative to the initial space of the vertices. Which is usually`
`+                model space. Since the yaw, pitch, and roll are usually defined relative to the`
`+                current orientation, that is what we need to do.</para>`
`+        </section>`
`     </section>`
`     <section>`
`         <title>Camera-Relative Orientation</title>`
`                 </inlineequation>.</para>`
`         </section>`
`     </section>`
`+    <section>`
`+        <title>Interpolation</title>`
`+        <para>One other trick you can do with quaternions is this.</para>`
`+    </section>`
`     `
`     <section>`
`         <?dbhtml filename="Tut08 In Review.html" ?>`

# File Tut 08 Getting Oriented/GimbalLock.cpp

` #include <glloader/gl_3_2_comp.h>`
` #include <GL/freeglut.h>`
` #include "../framework/framework.h"`
`+#include "../framework/Mesh.h"`
`+#include "../framework/MatrixStack.h"`
` #include <glm/glm.hpp>`
` #include <glm/gtc/type_ptr.hpp>`
` `
` 	return 1.0f / tan(fFovRad / 2.0f);`
` }`
` `
`-const float fFrustumScale = CalcFrustumScale(45.0f);`
`+const float fFrustumScale = CalcFrustumScale(20.0f);`
` `
` void InitializeProgram()`
` {`
` 	cameraToClipMatrixUnif = glGetUniformLocation(theProgram, "cameraToClipMatrix");`
` 	baseColorUnif = glGetUniformLocation(theProgram, "baseColor");`
` `
`-	float fzNear = 1.0f; float fzFar = 100.0f;`
`+	float fzNear = 1.0f; float fzFar = 600.0f;`
` `
` 	cameraToClipMatrix[0].x = fFrustumScale;`
` 	cameraToClipMatrix[1].y = fFrustumScale;`
` 	glUseProgram(0);`
` }`
` `
`-const int numberOfVertices = 24;`
`-`
`-#define FULL_COLOR 1.0f, 1.0f, 1.0f, 1.0f`
`-#define LIGHT_COLOR 0.75f, 0.75f, 0.75f, 1.0f`
`-#define MID_COLOR 0.5f, 0.5f, 0.5f, 1.0f`
`-#define DARK_COLOR 	0.3f, 0.3f, 0.3f, 1.0f`
`-`
`-`
`-const float vertexData[] =`
`-{`
`-	//Front`
`-	+0.5f, +0.5f, +0.5f,`
`-	+0.5f, -0.5f, +0.5f,`
`-	-0.5f, -0.5f, +0.5f,`
`-	-0.5f, +0.5f, +0.5f,`
`-`
`-	//Top`
`-	+0.5f, +0.5f, +0.5f,`
`-	-0.5f, +0.5f, +0.5f,`
`-	-0.5f, +0.5f, -0.5f,`
`-	+0.5f, +0.5f, -0.5f,`
`-`
`-	//Left`
`-	+0.5f, +0.5f, +0.5f,`
`-	+0.5f, +0.5f, -0.5f,`
`-	+0.5f, -0.5f, -0.5f,`
`-	+0.5f, -0.5f, +0.5f,`
`-`
`-	//Back`
`-	+0.5f, +0.5f, -0.5f,`
`-	-0.5f, +0.5f, -0.5f,`
`-	-0.5f, -0.5f, -0.5f,`
`-	+0.5f, -0.5f, -0.5f,`
`-`
`-	//Bottom`
`-	+0.5f, -0.5f, +0.5f,`
`-	+0.5f, -0.5f, -0.5f,`
`-	-0.5f, -0.5f, -0.5f,`
`-	-0.5f, -0.5f, +0.5f,`
`-`
`-	//Right`
`-	-0.5f, +0.5f, +0.5f,`
`-	-0.5f, -0.5f, +0.5f,`
`-	-0.5f, -0.5f, -0.5f,`
`-	-0.5f, +0.5f, -0.5f,`
`-`
`-`
`-	FULL_COLOR,`
`-	FULL_COLOR,`
`-	FULL_COLOR,`
`-	FULL_COLOR,`
`-`
`-	LIGHT_COLOR,`
`-	LIGHT_COLOR,`
`-	LIGHT_COLOR,`
`-	LIGHT_COLOR,`
`-`
`-	MID_COLOR,`
`-	MID_COLOR,`
`-	MID_COLOR,`
`-	MID_COLOR,`
`-`
`-	FULL_COLOR,`
`-	FULL_COLOR,`
`-	FULL_COLOR,`
`-	FULL_COLOR,`
`-`
`-	LIGHT_COLOR,`
`-	LIGHT_COLOR,`
`-	LIGHT_COLOR,`
`-	LIGHT_COLOR,`
`-`
`-	MID_COLOR,`
`-	MID_COLOR,`
`-	MID_COLOR,`
`-	MID_COLOR,`
`-};`
`-`
`-const GLshort indexData[] =`
`-{`
`-	0, 1, 2,`
`-	2, 3, 0,`
`-`
`-	4, 5, 6,`
`-	6, 7, 4,`
`-`
`-	8, 9, 10,`
`-	10, 11, 8,`
`-`
`-	12, 13, 14,`
`-	14, 15, 12,`
`-`
`-	16, 17, 18,`
`-	18, 19, 16,`
`-`
`-	20, 21, 22,`
`-	22, 23, 20,`
`-};`
`-`
`-GLuint vertexBufferObject;`
`-GLuint indexBufferObject;`
`-GLuint vao;`
`-`
`-void InitializeVAO()`
`-{`
`-	glGenBuffers(1, &vertexBufferObject);`
`-`
`-	glBindBuffer(GL_ARRAY_BUFFER, vertexBufferObject);`
`-	glBufferData(GL_ARRAY_BUFFER, sizeof(vertexData), vertexData, GL_STATIC_DRAW);`
`-	glBindBuffer(GL_ARRAY_BUFFER, 0);`
`-`
`-	glGenBuffers(1, &indexBufferObject);`
`-`
`-	glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, indexBufferObject);`
`-	glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(indexData), indexData, GL_STATIC_DRAW);`
`-	glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, 0);`
`-`
`-	glGenVertexArrays(1, &vao);`
`-	glBindVertexArray(vao);`
`-`
`-	size_t colorDataOffset = sizeof(float) * 3 * numberOfVertices;`
`-	glBindBuffer(GL_ARRAY_BUFFER, vertexBufferObject);`
`-	glEnableVertexAttribArray(positionAttrib);`
`-	glEnableVertexAttribArray(colorAttrib);`
`-	glVertexAttribPointer(positionAttrib, 3, GL_FLOAT, GL_FALSE, 0, 0);`
`-	glVertexAttribPointer(colorAttrib, 4, GL_FLOAT, GL_FALSE, 0, (void*)colorDataOffset);`
`-	glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, indexBufferObject);`
`-`
`-	glBindVertexArray(0);`
`-}`
`-`
`-inline float DegToRad(float fAngDeg)`
`-{`
`-	const float fDegToRad = 3.14159f * 2.0f / 360.0f;`
`-	return fAngDeg * fDegToRad;`
`-}`
`-`
`-inline float Clamp(float fValue, float fMinValue, float fMaxValue)`
`-{`
`-	if(fValue < fMinValue)`
`-		return fMinValue;`
`-`
`-	if(fValue > fMaxValue)`
`-		return fMaxValue;`
`-`
`-	return fValue;`
`-}`
`-`
`-glm::mat3 RotateX(float fAngDeg)`
`-{`
`-	float fAngRad = DegToRad(fAngDeg);`
`-	float fCos = cosf(fAngRad);`
`-	float fSin = sinf(fAngRad);`
`-`
`-	glm::mat3 theMat(1.0f);`
`-	theMat[1].y = fCos; theMat[2].y = -fSin;`
`-	theMat[1].z = fSin; theMat[2].z = fCos;`
`-	return theMat;`
`-}`
`-`
`-glm::mat3 RotateY(float fAngDeg)`
`-{`
`-	float fAngRad = DegToRad(fAngDeg);`
`-	float fCos = cosf(fAngRad);`
`-	float fSin = sinf(fAngRad);`
`-`
`-	glm::mat3 theMat(1.0f);`
`-	theMat[0].x = fCos; theMat[2].x = fSin;`
`-	theMat[0].z = -fSin; theMat[2].z = fCos;`
`-	return theMat;`
`-}`
`-`
`-glm::mat3 RotateZ(float fAngDeg)`
`-{`
`-	float fAngRad = DegToRad(fAngDeg);`
`-	float fCos = cosf(fAngRad);`
`-	float fSin = sinf(fAngRad);`
`-`
`-	glm::mat3 theMat(1.0f);`
`-	theMat[0].x = fCos; theMat[1].x = -fSin;`
`-	theMat[0].y = fSin; theMat[1].y = fCos;`
`-	return theMat;`
`-}`
`-`
`-class MatrixStack`
`-{`
`-public:`
`-	MatrixStack()`
`-		: m_currMat(1.0f)`
`-	{`
`-	}`
`-`
`-	const glm::mat4 &Top()`
`-	{`
`-		return m_currMat;`
`-	}`
`-`
`-	void RotateX(float fAngDeg)`
`-	{`
`-		m_currMat = m_currMat * glm::mat4(::RotateX(fAngDeg));`
`-	}`
`-`
`-	void RotateY(float fAngDeg)`
`-	{`
`-		m_currMat = m_currMat * glm::mat4(::RotateY(fAngDeg));`
`-	}`
`-`
`-	void RotateZ(float fAngDeg)`
`-	{`
`-		m_currMat = m_currMat * glm::mat4(::RotateZ(fAngDeg));`
`-	}`
`-`
`-	void Scale(const glm::vec3 &scaleVec)`
`-	{`
`-		glm::mat4 scaleMat(1.0f);`
`-		scaleMat[0].x = scaleVec.x;`
`-		scaleMat[1].y = scaleVec.y;`
`-		scaleMat[2].z = scaleVec.z;`
`-`
`-		m_currMat = m_currMat * scaleMat;`
`-	}`
`-`
`-	void Translate(const glm::vec3 &offsetVec)`
`-	{`
`-		glm::mat4 translateMat(1.0f);`
`-		translateMat[3] = glm::vec4(offsetVec, 1.0f);`
`-`
`-		m_currMat = m_currMat * translateMat;`
`-	}`
`-`
`-	void Push()`
`-	{`
`-		m_matrices.push(m_currMat);`
`-	}`
`-`
`-	void Pop()`
`-	{`
`-		m_currMat = m_matrices.top();`
`-		m_matrices.pop();`
`-	}`
`-`
`-private:`
`-	glm::mat4 m_currMat;`
`-	std::stack<glm::mat4> m_matrices;`
`-};`
`-`
`-void DrawGimbalSides(MatrixStack &currMatrix, float fGimbalSidesOffset, float fGimbalSidesScale)`
`-{`
`-	//Draw the top`
`-	{`
`-		currMatrix.Push();`
`-		currMatrix.Translate(glm::vec3(0.0f, fGimbalSidesOffset, 0.0f));`
`-		currMatrix.Scale(glm::vec3(fGimbalSidesScale, 1.0f, 1.0f));`
`-		glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`-		glDrawElements(GL_TRIANGLES, ARRAY_COUNT(indexData), GL_UNSIGNED_SHORT, 0);`
`-		currMatrix.Pop();`
`-	}`
`-`
`-	//Draw the bottom`
`-	{`
`-		currMatrix.Push();`
`-		currMatrix.Translate(glm::vec3(0.0f, -fGimbalSidesOffset, 0.0f));`
`-		currMatrix.Scale(glm::vec3(fGimbalSidesScale, 1.0f, 1.0f));`
`-		glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`-		glDrawElements(GL_TRIANGLES, ARRAY_COUNT(indexData), GL_UNSIGNED_SHORT, 0);`
`-		currMatrix.Pop();`
`-	}`
`-`
`-	//Draw the right`
`-	{`
`-		currMatrix.Push();`
`-		currMatrix.Translate(glm::vec3(fGimbalSidesOffset, 0.0f, 0.0f));`
`-		currMatrix.Scale(glm::vec3(1.0f, fGimbalSidesScale, 1.0f));`
`-		glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`-		glDrawElements(GL_TRIANGLES, ARRAY_COUNT(indexData), GL_UNSIGNED_SHORT, 0);`
`-		currMatrix.Pop();`
`-	}`
`-`
`-	//Draw the left`
`-	{`
`-		currMatrix.Push();`
`-		currMatrix.Translate(glm::vec3(-fGimbalSidesOffset, 0.0f, 0.0f));`
`-		currMatrix.Scale(glm::vec3(1.0f, fGimbalSidesScale, 1.0f));`
`-		glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`-		glDrawElements(GL_TRIANGLES, ARRAY_COUNT(indexData), GL_UNSIGNED_SHORT, 0);`
`-		currMatrix.Pop();`
`-	}`
`-}`
`-`
`-void DrawGimbalAttachments(MatrixStack &currMatrix, float fGimbalAttachOffset)`
`-{`
`-	//Draw the right attachment.`
`-	{`
`-		currMatrix.Push();`
`-		currMatrix.Translate(glm::vec3(fGimbalAttachOffset, 0.0f, 0.0f));`
`-		currMatrix.Scale(glm::vec3(1.0f, 0.5f, 0.5f));`
`-		glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`-		glDrawElements(GL_TRIANGLES, ARRAY_COUNT(indexData), GL_UNSIGNED_SHORT, 0);`
`-		currMatrix.Pop();`
`-	}`
`-`
`-	//Draw the left attachment.`
`-	{`
`-		currMatrix.Push();`
`-		currMatrix.Translate(glm::vec3(-fGimbalAttachOffset, 0.0f, 0.0f));`
`-		currMatrix.Scale(glm::vec3(1.0f, 0.5f, 0.5f));`
`-		glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`-		glDrawElements(GL_TRIANGLES, ARRAY_COUNT(indexData), GL_UNSIGNED_SHORT, 0);`
`-		currMatrix.Pop();`
`-	}`
`-}`
`-`
`-`
`-void DrawBaseGimbal(MatrixStack &currMatrix, float fSize, glm::vec4 baseColor)`
`-{`
`-	//A Gimbal can only be 4 units in size or more.`
`-	assert(fSize > 4.0f);`
`-`
`-	glUseProgram(theProgram);`
`-	//Set the base color for this object.`
`-	glUniform4fv(baseColorUnif, 1, glm::value_ptr(baseColor));`
`-	glBindVertexArray(vao);`
`-`
`-	float fGimbalSidesOffset = (fSize / 2.0f) - 1.5f;`
`-	float fGimbalSidesScale = fSize - 2.0f;`
`-`
`-	DrawGimbalSides(currMatrix, fGimbalSidesOffset, fGimbalSidesScale);`
`-	`
`-	float fGimbalAttachOffset = (fSize / 2.0f) - 0.5f;`
`-`
`-	DrawGimbalAttachments(currMatrix, fGimbalAttachOffset);`
`-`
`-	glBindVertexArray(0);`
`-	glUseProgram(0);`
`-}`
`-`
` enum GimbalAxis`
` {`
` 	GIMBAL_X_AXIS,`
` 	GIMBAL_Z_AXIS,`
` };`
` `
`-void DrawGimbal(MatrixStack &currMatrix, GimbalAxis eAxis, float fSize, glm::vec4 baseColor)`
`+Framework::Mesh *g_Gimbals[3] = {NULL, NULL, NULL};`
`+const char *g_strGimbalNames[3] =`
` {`
`-	currMatrix.Push();`
`+	"LargeGimbal.xml",`
`+	"MediumGimbal.xml",`
`+	"SmallGimbal.xml",`
`+};`
`+`
`+void DrawGimbal(Framework::MatrixStack &currMatrix, GimbalAxis eAxis, float fSize, glm::vec4 baseColor)`
`+{`
`+	Framework::MatrixStackPusher pusher(currMatrix);`
` `
` 	switch(eAxis)`
` 	{`
` 		break;`
` 	}`
` `
`-	DrawBaseGimbal(currMatrix, fSize, baseColor);`
`-	currMatrix.Pop();`
`+	glUseProgram(theProgram);`
`+	//Set the base color for this object.`
`+	glUniform4fv(baseColorUnif, 1, glm::value_ptr(baseColor));`
`+	glUniformMatrix4fv(modelToCameraMatrixUnif, 1, GL_FALSE, glm::value_ptr(currMatrix.Top()));`
`+`
`+	g_Gimbals[eAxis]->Render();`
`+`
`+	glUseProgram(0);`
` }`
` `
` //Called after the window and OpenGL are initialized. Called exactly once, before the main loop.`
` void init()`
` {`
` 	InitializeProgram();`
`-	InitializeVAO();`
`+`
`+	try`
`+	{`
`+		for(int iLoop = 0; iLoop < 3; iLoop++)`
`+		{`
`+			g_Gimbals[iLoop] = new Framework::Mesh(g_strGimbalNames[iLoop]);`
`+		}`
`+	}`
`+	catch(std::exception &except)`
`+	{`
`+		printf(except.what());`
`+	}`
` `
` `
` 	glEnable(GL_CULL_FACE);`
` 	glClearDepth(1.0f);`
` 	glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);`
` `
`-	MatrixStack currMatrix;`
`-	currMatrix.Translate(glm::vec3(0.0f, 0.0f, -60.0f));`
`+	Framework::MatrixStack currMatrix;`
`+	currMatrix.Translate(glm::vec3(0.0f, 0.0f, -200.0f));`
` 	currMatrix.RotateX(g_angles.fAngleX);`
` 	DrawGimbal(currMatrix, GIMBAL_X_AXIS, 30.0f, glm::vec4(0.4f, 0.4f, 1.0f, 1.0f));`
` 	currMatrix.RotateY(g_angles.fAngleY);`

# File Tut 08 Getting Oriented/data/GenGimbals.lua

`+require "XmlWriter"`
`+require "vmath"`
`+`
`+local function GenStringFromArray(theArray)`
`+	local array = {" "}`
`+	for i, vector in ipairs(theArray) do`
`+		array[#array + 1] = "        " .. table.concat(vector, " ");`
`+	end`
`+	`
`+	return table.concat(array, "\n");`
`+end`
`+`
`+local iSegCount = ...;`
`+iSegCount = iSegCount or 40;`
`+`
`+local gimbalPoints = {{}, {}, {}};`
`+local gimbalColors = {{}, {}, {}};`
`+local gimbalRadii = {28, 24, 20};`
`+local gimbalConnect = {4, 4, 4};`
`+local gimbalTriStrips = {{}, {}, {}, {}};`
`+local gimbalTris = {};`
`+local gimbalNames = {"Large", "Medium", "Small"};`
`+`
`+local iAngle = 3.14159 * 2.0 / iSegCount;`
`+`
`+--Compute circle attributes.`
`+local function AddSegments(SegmentFunc)`
`+	for iSeg = 1, iSegCount do`
`+		local iCurrAngle = iSeg * iAngle;`
`+		local radialDir = vmath.vec2(math.cos(iCurrAngle), math.sin(iCurrAngle));`
`+		`
`+		for iGimbal = 1, #gimbalRadii do`
`+			local vShort = radialDir * (gimbalRadii[iGimbal] - 1.0);`
`+			local vLong = radialDir * (gimbalRadii[iGimbal] + 1.0);`
`+			`
`+			SegmentFunc(iGimbal, vShort, vLong)`
`+		end`
`+	end`
`+end`
`+`
`+local halfHeight = 1.0;`
`+`
`+local SegmentAdders =`
`+{`
`+	function (iGimbal, vShort, vLong)`
`+		local iLen = #gimbalPoints[iGimbal];`
`+		gimbalPoints[iGimbal][iLen + 1] = vmath.vec3(vLong[1], vLong[2], halfHeight);`
`+		gimbalPoints[iGimbal][iLen + 2] = vmath.vec3(vShort[1], vShort[2], halfHeight);`
`+		gimbalColors[iGimbal][iLen + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+		gimbalColors[iGimbal][iLen + 2] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	end,`
`+	function (iGimbal, vShort, vLong)`
`+		local iLen = #gimbalPoints[iGimbal];`
`+		gimbalPoints[iGimbal][iLen + 1] = vmath.vec3(vShort[1], vShort[2], halfHeight);`
`+		gimbalPoints[iGimbal][iLen + 2] = vmath.vec3(vShort[1], vShort[2], -halfHeight);`
`+		gimbalColors[iGimbal][iLen + 1] = vmath.vec4(0.5, 0.5, 0.5, 1.0);`
`+		gimbalColors[iGimbal][iLen + 2] = vmath.vec4(0.5, 0.5, 0.5, 1.0);`
`+	end,`
`+	function (iGimbal, vShort, vLong)`
`+		local iLen = #gimbalPoints[iGimbal];`
`+		gimbalPoints[iGimbal][iLen + 1] = vmath.vec3(vShort[1], vShort[2], -halfHeight);`
`+		gimbalPoints[iGimbal][iLen + 2] = vmath.vec3(vLong[1], vLong[2], -halfHeight);`
`+		gimbalColors[iGimbal][iLen + 1] = vmath.vec4(0.9, 0.9, 0.9, 1.0);`
`+		gimbalColors[iGimbal][iLen + 2] = vmath.vec4(0.9, 0.9, 0.9, 1.0);`
`+	end,`
`+	function (iGimbal, vShort, vLong)`
`+		local iLen = #gimbalPoints[iGimbal];`
`+		gimbalPoints[iGimbal][iLen + 1] = vmath.vec3(vLong[1], vLong[2], -halfHeight);`
`+		gimbalPoints[iGimbal][iLen + 2] = vmath.vec3(vLong[1], vLong[2], halfHeight);`
`+		gimbalColors[iGimbal][iLen + 1] = vmath.vec4(0.75, 0.75, 0.75, 1.0);`
`+		gimbalColors[iGimbal][iLen + 2] = vmath.vec4(0.75, 0.75, 0.75, 1.0);`
`+	end,`
`+}`
`+`
`+for i, adder in ipairs(SegmentAdders) do`
`+	AddSegments(adder);`
`+end`
`+`
`+--Add the connecting pieces, on the left and right.`
`+local conSize = halfHeight * 0.6;`
`+local function AddConnector(radius, offset, points, color)`
`+	--Inside the current gimbal`
`+	points[#points + 1] = vmath.vec3(radius, conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius, -conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius, -conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius, conSize, -conSize);`
`+	`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+`
`+	--Inside the outer gimbal.`
`+	points[#points + 1] = vmath.vec3(radius + offset, conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, -conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, -conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, conSize, -conSize);`
`+	`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	`
`+	--Front.`
`+	points[#points + 1] = vmath.vec3(radius, conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius, -conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, -conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, conSize, conSize);`
`+	`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	color[#color + 1] = vmath.vec4(1.0, 1.0, 1.0, 1.0);`
`+	`
`+	--Back.`
`+	points[#points + 1] = vmath.vec3(radius, conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius, -conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, -conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, conSize, -conSize);`
`+	`
`+	color[#color + 1] = vmath.vec4(0.9, 0.9, 0.9, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.9, 0.9, 0.9, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.9, 0.9, 0.9, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.9, 0.9, 0.9, 1.0);`
`+	`
`+	--Top.`
`+	points[#points + 1] = vmath.vec3(radius, conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius, conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, conSize, conSize);`
`+	`
`+	color[#color + 1] = vmath.vec4(0.75, 0.75, 0.75, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.75, 0.75, 0.75, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.75, 0.75, 0.75, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.75, 0.75, 0.75, 1.0);`
`+	`
`+	--Bottom.`
`+	points[#points + 1] = vmath.vec3(radius, -conSize, conSize);`
`+	points[#points + 1] = vmath.vec3(radius, -conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, -conSize, -conSize);`
`+	points[#points + 1] = vmath.vec3(radius + offset, -conSize, conSize);`
`+	`
`+	color[#color + 1] = vmath.vec4(0.5, 0.5, 0.5, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.5, 0.5, 0.5, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.5, 0.5, 0.5, 1.0);`
`+	color[#color + 1] = vmath.vec4(0.5, 0.5, 0.5, 1.0);`
`+end`
`+`
`+for iGimbal = 1, #gimbalRadii do`
`+	local points = gimbalPoints[iGimbal];`
`+	local colors = gimbalColors[iGimbal];`
`+`
`+	--Right connector.`
`+	AddConnector(gimbalRadii[iGimbal], gimbalConnect[iGimbal],`
`+		gimbalPoints[iGimbal], gimbalColors[iGimbal]);`
`+	`
`+	--Left connector.`
`+	AddConnector(-gimbalRadii[iGimbal], -gimbalConnect[iGimbal],`
`+		gimbalPoints[iGimbal], gimbalColors[iGimbal]);`
`+end`
`+`
`+--Compute strips.`
`+--Number of attributes that each circle strip takes.`
`+local indexOffset = iSegCount * 2;`
`+local function AddStripIndices(strip, baseIndex, stripIx)`
`+	strip[#strip + 1] = baseIndex + indexOffset * stripIx;`
`+	strip[#strip + 1] = baseIndex + indexOffset * stripIx + 1;`
`+end`
`+`
`+`
`+for iSeg = 1, iSegCount do`
`+	local baseIndex = ((iSeg - 1) * 2);`
`+	AddStripIndices(gimbalTriStrips[1], baseIndex, 0);`
`+	AddStripIndices(gimbalTriStrips[2], baseIndex, 1);`
`+	AddStripIndices(gimbalTriStrips[3], baseIndex, 2);`
`+	AddStripIndices(gimbalTriStrips[4], baseIndex, 3);`
`+end`
`+`
`+local lastStripIndex = iSegCount * 2;`
`+AddStripIndices(gimbalTriStrips[1], 0, 0);`
`+AddStripIndices(gimbalTriStrips[2], 0, 1);`
`+AddStripIndices(gimbalTriStrips[3], 0, 2);`
`+AddStripIndices(gimbalTriStrips[4], 0, 3);`
`+`
`+local firstTriIndex = indexOffset * 4;`
`+local numValuesPerConnecter = 24;`
`+`
`+local connectTris = {`
`+--Inside the current gimbal`
`+	0, 1, 2,`
`+	2, 3, 0,`
`+--Inside the outer gimbal.`
`+	4, 6, 5,`
`+	6, 4, 7,`
`+--Front.`
`+	8, 10, 9,`
`+	11, 10, 8,`
`+--Back.`
`+	12, 13, 14,`
`+	15, 12, 14,`
`+--Top.`
`+	16, 17, 18,`
`+	18, 19, 16,`
`+--Bottom.`
`+	20, 22, 21,`
`+	22, 20, 23,`
`+}`
`+`
`+for i=1, #connectTris, 3 do`
`+	connectTris[#connectTris + 1] = connectTris[i] + numValuesPerConnecter;`
`+	connectTris[#connectTris + 1] = connectTris[i + 2] + numValuesPerConnecter;`
`+	connectTris[#connectTris + 1] = connectTris[i + 1] + numValuesPerConnecter;`
`+end`
`+`
`+for i, index in ipairs(connectTris) do`
`+	gimbalTris[#gimbalTris + 1] = firstTriIndex + index;`
`+end`
`+`
`+`
`+`
`+--Write the gimbal to the file.`
`+local function WriteGimbal(iGimbal)`
`+	local writer = XmlWriter.XmlWriter(gimbalNames[iGimbal] .. "Gimbal.xml");`
`+	writer:AddPI("oxygen", [[RNGSchema="../../Documents/meshFormat.rnc" type="compact"]]);`
`+	writer:PushElement("mesh", "http://www.arcsynthesis.com/gltut/mesh");`
`+		writer:PushElement("attribute");`
`+			writer:AddAttribute("index", "0");`
`+			writer:AddAttribute("type", "float");`
`+			writer:AddAttribute("size", "3");`
`+			writer:AddText(GenStringFromArray(gimbalPoints[iGimbal]));`
`+		writer:PopElement();`
`+		writer:PushElement("attribute");`
`+			writer:AddAttribute("index", "1");`
`+			writer:AddAttribute("type", "float");`
`+			writer:AddAttribute("size", "4");`
`+			writer:AddText(GenStringFromArray(gimbalColors[iGimbal]));`
`+		writer:PopElement();`
`+		for iStrip = 1, #gimbalTriStrips do`
`+			writer:PushElement("indices");`
`+				writer:AddAttribute("cmd", "tri-strip");`
`+				writer:AddAttribute("type", "ushort");`
`+				writer:AddText(table.concat(gimbalTriStrips[iStrip], " "));`
`+			writer:PopElement();`
`+		end`
`+		if(#gimbalTris > 0) then`
`+			writer:PushElement("indices");`
`+				writer:AddAttribute("cmd", "triangles");`
`+				writer:AddAttribute("type", "ushort");`
`+				writer:AddText(table.concat(gimbalTris, " "));`
`+			writer:PopElement();`
`+		end`
`+	writer:PopElement();`
`+	writer:Close();`
`+end`
`+`
`+for iGimbal = 1, #gimbalRadii do`
`+	WriteGimbal(iGimbal);`
`+end`

# File Tut 08 Getting Oriented/data/LargeGimbal.xml

`+<?xml version="1.0" encoding="UTF-8"?>`
`+<?oxygen RNGSchema="../../Documents/meshFormat.rnc" type="compact"?>`
`+`
`+<mesh xmlns="http://www.arcsynthesis.com/gltut/mesh" >`
`+	<attribute index="0" type="float" size="3" > `
`+        28.642962479172 4.5365956858331 1`
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# File Tut 08 Getting Oriented/data/MediumGimbal.xml

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