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POAngle between two 3D vectors
 

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  1. POAngle between two 3D vectors
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    <p>I have a series of vertices (pink) that I want to rotate so that one edge of the pattern of vertices matches with the edge of the triangle (white).</p> <p>To do this, I first create two vectors to represent the edges: floretAB and triangleAB (green). I then find the cross product of the two to get an axis around which I can rotate the vertices (red).</p> <p>I then get the angle between the two vectors, and use that, with the rotation axis to create a quaternion. Finally, I rotate all the vertices around the quaternion.</p> <p><img src="https://i.stack.imgur.com/N2el6.png" alt="enter image description here"> </p> <p><em>Before rotation</em></p> <p>_</p> <p><img src="https://i.stack.imgur.com/aNVdV.png" alt="enter image description here"> </p> <p><em>What rotation should produce</em></p> <p>_</p> <p>However, although the vertices correctly rotate around the quaternion, the angle is not coming out correct, as illustrated here:</p> <p><img src="https://i.stack.imgur.com/B5tci.png" alt="enter image description here"></p> <p>This is the code I'm using to get the angle between the two vectors. I don't understand what I'm doing wrong:</p> <pre><code>double[] cross = new double[3]; crossProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ, cross); double dot = dotProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ); double crossMag = Math.sqrt(cross[0]*cross[0] + cross[1]*cross[1] + cross[2]*cross[2]); double angle = Math.atan2(crossMag, dot); public static double dotProduct(double vector1X,double vector1Y,double vector1Z,double vector2X,double vector2Y,double vector2Z){ return vector1X*vector2X + vector1Y*vector2Y + vector1Z*vector2Z; } public static void crossProduct(double vector1X,double vector1Y,double vector1Z,double vector2X,double vector2Y,double vector2Z, double[] outputArray){ outputArray[0] = vector1Y*vector2Z - vector1Z*vector2Y; outputArray[1] = vector1Z*vector2X - vector1X*vector2Z; outputArray[2] = vector1X*vector2Y - vector1Y*vector2X; } </code></pre> <p>Any help with this would be most appreciated as it is really bugging me. </p> <p>Thanks, James</p> <p><strong>Edit:</strong> Here is the rest of the code:</p> <pre><code> // get floret p1,p2 vector // get triangle p1,p2 vector Vector3D floretAB = new Vector3D(florets3D[0], florets3D[7]); // get triangle p1,p2 vector Vector3D triangleAB = new Vector3D(triangle[0], triangle[1]); // get rotation axis (cross) and angle (dot) /* double[] cross = new double[3]; crossProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ, cross); double dotMag = floretAB.getMagnitude() * triangleAB.getMagnitude(); double dot = dotProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ) / dotMag; double angle = Math.acos(dot); */ double[] cross = new double[3]; crossProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ, cross); double dot = dotProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ); double crossMag = Math.sqrt(cross[0]*cross[0] + cross[1]*cross[1] + cross[2]*cross[2]); double angle = Math.atan2(crossMag, dot); // rotate floret so p1,p2 vector matches with triangle p1,p2 vector double[] newVerts = new double[3]; Quaternion quat = new Quaternion(cross[0], cross[1], cross[2], angle); for(int i = 0;i&lt;numfloretVerts;i++){ Vertex3D vert = florets3D[i]; quat.RotateVector(vert.getmX(), vert.getmY(), vert.getmZ(), newVerts); vert.setmX(newVerts[0]); vert.setmY(newVerts[1]); vert.setmZ(newVerts[2]); } </code></pre> <p>_</p> <pre><code>public class Vector3D { public double mX; public double mY; public double mZ; public Vertex3D point; /** * Constructs a vector from two points. The new vector is normalised * * @param point1 * @param point2 */ public Vector3D(Vertex3D point1, Vertex3D point2){ mX = point2.getmX() - point1.getmX(); mY = point2.getmY() - point1.getmY(); mZ = point2.getmZ() - point1.getmZ(); normalise(); point = point1; } /** * Normalises the vector */ public void normalise(){ double magnitude = Math.sqrt(mX*mX + mY*mY + mZ*mZ); if(magnitude!=0){ mX /= magnitude; mY /= magnitude; mZ /= magnitude; } } /** * * @return the magnitude of the vector */ public double getMagnitude(){ return Math.sqrt(mX*mX + mY*mY + mZ*mZ); } } </code></pre> <p>_</p> <pre><code>public class Quaternion { private static final double TOLERANCE = 0.00001f; double w; double x; double y; double z; public Quaternion(double axisX, double axisY, double axisZ, double angleInRadians){ setAxisAngle(axisX, axisY, axisZ, angleInRadians); } public void Normalise(){ // Don't normalize if we don't have to double mag2 = w * w + x * x + y * y + z * z; if (Math.abs(mag2) &gt; TOLERANCE &amp;&amp; Math.abs(mag2 - 1.0f) &gt; TOLERANCE) { double mag = (double) Math.sqrt(mag2); w /= mag; x /= mag; y /= mag; z /= mag; } } public void getConjugate(double[] outputArray){ outputArray[0] = w; outputArray[1] = -x; outputArray[2] = -y; outputArray[3] = -z; } public void Multiply(double[] aq, double[] rq, double[] outputArray){ outputArray[0] = aq[0] * rq[0] - aq[1] * rq[1] - aq[2] * rq[2] - aq[3] * rq[3]; outputArray[1] = aq[0] * rq[1] + aq[1] * rq[0] + aq[2] * rq[3] - aq[3] * rq[2]; outputArray[2] = aq[0] * rq[2] + aq[2] * rq[0] + aq[3] * rq[1] - aq[1] * rq[3]; outputArray[3] = aq[0] * rq[3] + aq[3] * rq[0] + aq[1] * rq[2] - aq[2] * rq[1]; } private double[] vecQuat = new double[4]; private double[] resQuat = new double[4]; private double[] thisQuat = new double[4]; private double[] conj = new double[4]; /** * Rotates a vector (or point) around this axis-angle * * @param vectorX the x component of the vector (or point) * @param vectorY the y component of the vector (or point) * @param vectorZ the z component of the vector (or point) * @param outputArray the array in which the results will be stored */ public void RotateVector(double vectorX, double vectorY, double vectorZ, double[] outputArray){ vecQuat[0] = 0.0f; vecQuat[1] = vectorX; vecQuat[2] = vectorY; vecQuat[3] = vectorZ; thisQuat[0] = w; thisQuat[1] = x; thisQuat[2] = y; thisQuat[3] = z; getConjugate(conj); Multiply(vecQuat,conj,resQuat); Multiply(thisQuat,resQuat,vecQuat); outputArray[0] = vecQuat[1]; outputArray[1] = vecQuat[2]; outputArray[2] = vecQuat[3]; } /** * set Quaternion by providing axis-angle form */ public void setAxisAngle(double axisX, double axisY, double axisZ, double angleInRadians){ w = (double) Math.cos( angleInRadians/2); x = (double) (axisX * Math.sin( angleInRadians/2 )); y = (double) (axisY * Math.sin( angleInRadians/2 )); z = (double) (axisZ * Math.sin( angleInRadians/2 )); Normalise(); } } </code></pre>
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    1. PO
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      1. PTAnswer
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    1. PTQuestion
    1. USJames Coote
    1. USJames Coote
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    1. This table or related slice is empty.
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    2. PO
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    1. VO
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      1. POAngle between two 3D vectors
      1. USandrewpey
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    2. VO
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      1. POAngle between two 3D vectors
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      1. VTUpMod
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      1. VTUpMod
    1. COTry `Math.atan2(dot, crossMag);`
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      1. POAngle between two 3D vectors
      1. USJohn Dvorak
    2. CODidn't make a difference / solve the problem :(
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      1. POAngle between two 3D vectors
      1. USJames Coote
 

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