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POOptimize Normalmap rotation of a vector
 

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  1. POOptimize Normalmap rotation of a vector
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    <p>I use a quaternion to rotate the normal vector of a mesh into the direction the normal map vector. I thought I could use the Quaternion. So I create a quaternion with the angle between the normal of the mesh and (0,0,1). Shortened the methods in libgdx, creation of the Quaternion looks like this</p> <pre><code>vec4 createQuaternion(vec3 normal) { float l_ang = acos(clamp(normal.z, -CONST_ONE, CONST_ONE))/CONST_TWO; float l_sin = sin(l_ang); return normalize(vec4(-normal.y * l_sin, normal.x * l_sin, CONST_ZERO, cos(l_ang))); } </code></pre> <p>with this Quaternion I can rotate the normal of the mesh in the direction of the normal map. Therefore I use a method I've seen in the libgdx Quaternion (while v is the normal from the normalmap and m is the quaternion):</p> <pre><code>vec3 rotateNormal(vec3 v, vec4 m) { vec4 tmp1 = vec4(v,CONST_ZERO); vec4 tmp2 = vec4(m); // conjugate tmp2.x = -tmp2.x; tmp2.y = -tmp2.y; tmp2.z = -tmp2.z; tmp2 = mulLeft(tmp1, tmp2); tmp1 = mulLeft(m, tmp2); v.x = tmp1.x; v.y = tmp1.y; v.z = tmp1.z; return v; } </code></pre> <p>The method mulLeft looks like that:</p> <pre><code>vec4 mulLeft(vec4 q, vec4 a) { float newX = q.w * a.x + q.x * a.w + q.y * a.z - q.z * a.y; float newY = q.w * a.y + q.y * a.w + q.z * a.x - q.x * a.z; float newZ = q.w * a.z + q.z * a.w + q.x * a.y - q.y * a.x; float newW = q.w * a.w - q.x * a.x - q.y * a.y - q.z * a.z; a.x = newX; a.y = newY; a.z = newZ; a.w = newW; return a; } </code></pre> <p>For the use in the shader I just call:</p> <pre><code>normal = rotateNormal(normalMap, createQuaternion(normalMesh)); </code></pre> <p>and <strong>it works as expected</strong>.</p> <p>The only thing I am considered about is that I can imagine that there is a shorter way to write that. Especially the mulLeft Method. Is there?</p> <p>What do you think about the whole method, turning the vector by quaternion instead of using NTB? ntb looks a bit like too much calculation while animating the mesh.</p> <p>Edit: This is the a test with my sourcecode</p> <p><img src="https://i.stack.imgur.com/a569j.png" alt="My Code"></p> <p>This is a Test with Tenfour's suggestion</p> <p><img src="https://i.stack.imgur.com/OxpEB.png" alt=""></p> <p>Edit2:</p> <p>I shortened the whole thing to:</p> <pre><code>vec3 rotateNormal(vec3 normalMap, vec3 normal) { // create quaternion from cross(normal, vec3(0,0,1)) float l_ang = acos(clamp(normal.z, -CONST_ONE, CONST_ONE))/CONST_TWO; float l_sin = sin(l_ang); vec4 quat = normalize(vec4(-normal.y * l_sin, normal.x * l_sin, CONST_ZERO, cos(l_ang))); // shortened function to double mulQuat the normalMap on the quaternion return vec3( quat.x*quat.x*normalMap.x - quat.y*quat.y*normalMap.x - quat.z*quat.z*normalMap.x + quat.w*quat.w*normalMap.x - CONST_TWO*quat.z*quat.w*normalMap.y + CONST_TWO*quat.y*quat.w*normalMap.z + CONST_TWO*quat.x *(quat.y*normalMap.y + quat.z*normalMap.z), -(quat.x*quat.x*normalMap.y) - quat.z*quat.z* normalMap.y + (quat.y*quat.y + quat.w*quat.w ) * normalMap.y + CONST_TWO*quat.z *(quat.w*normalMap.x + quat.y*normalMap.z) + CONST_TWO*quat.x* (quat.y*normalMap.x - quat.w*normalMap.z), quat.y*(-CONST_TWO*quat.w*normalMap.x + CONST_TWO*quat.z*normalMap.y) + CONST_TWO*quat.x*(quat.z*normalMap.x + quat.w*normalMap.y) - quat.x*quat.x*normalMap.z - quat.y*quat.y*normalMap.z + (quat.z*quat.z + quat.w*quat.w )* normalMap.z ); } </code></pre> <p>Input is the normal from the normal map and the normal of the mesh. I am sure there's something better than that. what could that be?</p>
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