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POOpenGL - Rotate a 'Curve' About the Y-Axis
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  1. POOpenGL - Rotate a 'Curve' About the Y-Axis
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    copied!<p><em>As per my <a href="https://math.stackexchange.com/questions/75951/computing-points-in-3d-space">question</a> on Math Stackexchange:</em></p> <p>I am working on a project for my 3D Graphics class. The project is built with C++ and OpenGL / Glut. Basically, I create a horizontal rectangle window, subdivided into two squares. On the left, I have a two dimensional coordinate plane, which allows the users to point and click and define a profile 'curve'. I then need to wrap this curve around the Y-axis n number of times. </p> <p>So, would anyone be able to guide me as to how I would use Trigonometry to calculate the X and Z values of the successive points? If for example, a user clicks and creates the point:</p> <p>(1, 1, 0)</p> <p>And their sweep resolution (n) is set to, say, 10, then I need to redraw that point every 36 (360/10) degrees around the Y-axis.</p> <p>Am I correct in assuming that Trigonometry will help me here? If so, can someone please enlighten me a bit as to how to calculate the location of a translated point in 3D space? It's been a while since I took Trig, and I don't believe we ever left 2D space.</p> <p><strong>EDIT</strong>: I attempted to use:</p> <pre><code>x'=xcos(theta)-zsin(theta) y'=y z'=xsin(theta)+zcos(theta) </code></pre> <p>, as per my understanding of AMPerrine's <a href="https://math.stackexchange.com/questions/75951/computing-points-in-3d-space/75958#75958">answer</a>, and I don't think it worked as I'd hoped:</p> <pre><code>// this is in a loop // setup the new angle double angle = i&gt;0 ? (360/sweepResolutionMod)*i : 0; angle = angle * (M_PI/180); // for each point... for( int i=0; i&lt;clickedPoints.size(); i++ ) { // initial point, normalized GLfloat tempX = (clickedPoints[i].x-250)/250; GLfloat tempY = (clickedPoints[i].y-250)/250; GLfloat tempZ = 0.0; // log the initial point cout &lt;&lt; "(" &lt;&lt; tempX &lt;&lt; ", " &lt;&lt; tempY &lt;&lt; ", 0.0) by " &lt;&lt; angle &lt;&lt; " radians = "; // generate the new point GLfloat newX = (tempX * cos(angle)) - (tempZ * sin(angle)); GLfloat newY = tempY; GLfloat newZ = (tempX * sin(angle)) - (tempZ * cos(angle)); // log the new point cout &lt;&lt; "(" &lt;&lt; newX &lt;&lt; ", " &lt;&lt; newY &lt;&lt; ", " &lt;&lt; newZ &lt;&lt; ")\n"; // render the new point glVertex3d(newX, newY, newZ); } </code></pre> <p>This produces no screen output, but console output of:</p> <pre><code>(0.048, -0.296, 0.0) by 0 radians = (0.048, -0.296, 0) (0.376, -0.508, 0.0) by 0 radians = (0.376, -0.508, 0) (0.72, -0.204, 0.0) by 0 radians = (0.72, -0.204, 0) (0.652, 0.176, 0.0) by 0 radians = (0.652, 0.176, 0) (0.368, 0.504, 0.0) by 0 radians = (0.368, 0.504, 0) (0.048, -0.296, 0.0) by 0.628319 radians = (0.0388328, -0.296, 0.0282137) (0.376, -0.508, 0.0) by 0.628319 radians = (0.30419, -0.508, 0.221007) (0.72, -0.204, 0.0) by 0.628319 radians = (0.582492, -0.204, 0.423205) (0.652, 0.176, 0.0) by 0.628319 radians = (0.527479, 0.176, 0.383236) (0.368, 0.504, 0.0) by 0.628319 radians = (0.297718, 0.504, 0.216305) (0.048, -0.296, 0.0) by 1.25664 radians = (0.0148328, -0.296, 0.0456507) (0.376, -0.508, 0.0) by 1.25664 radians = (0.11619, -0.508, 0.357597) (0.72, -0.204, 0.0) by 1.25664 radians = (0.222492, -0.204, 0.684761) (0.652, 0.176, 0.0) by 1.25664 radians = (0.201479, 0.176, 0.620089) (0.368, 0.504, 0.0) by 1.25664 radians = (0.113718, 0.504, 0.349989) ... (0.048, -0.296, 0.0) by 6.28319 radians = (0.048, -0.296, -1.17566e-17) (0.376, -0.508, 0.0) by 6.28319 radians = (0.376, -0.508, -9.20934e-17) (0.72, -0.204, 0.0) by 6.28319 radians = (0.72, -0.204, -1.76349e-16) (0.652, 0.176, 0.0) by 6.28319 radians = (0.652, 0.176, -1.59694e-16) (0.368, 0.504, 0.0) by 6.28319 radians = (0.368, 0.504, -9.0134e-17) </code></pre> <p>I'm not sure what exactly is going on here, but I'm having a terrible time trying to figure it out, so please don't think I'm trying to get double reputation or anything, I'm just really stuck.</p> <p><strong>EDIT</strong> 2: Here is my whole display routine for my perspective subview:</p> <pre><code>void displayPersp(void) { glClear(GL_COLOR_BUFFER_BIT); glMatrixMode (GL_MODELVIEW); glLoadIdentity (); gluLookAt (-2.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0); // draw the axis glBegin(GL_LINES); // x glVertex3f(500.0, 0.0, 0.0); glVertex3f(-500.0, 0.0, 0.0); // y glVertex3f(0.0, -500.0, 0.0); glVertex3f(0.0, 500.0, 0.0); // z glVertex3f(0.0, 0.0, -500.0); glVertex3f(0.0, 0.0, 500.0); glEnd(); cout &lt;&lt; endl; // loop as many number of times as we are going to draw the points around the Y-Axis for( int i=0; i&lt;=sweepResolutionMod; i++ ) { cout &lt;&lt; endl; // setup the new angle double angle = i&gt;0 ? (360/sweepResolutionMod)*i : 0; angle = angle * (M_PI/180); // for each point... for( int i=0; i&lt;clickedPoints.size(); i++ ) { GLfloat tempX = (clickedPoints[i].x-250)/250; GLfloat tempY = (clickedPoints[i].y-250)/250; GLfloat tempZ = 0.0; cout &lt;&lt; "(" &lt;&lt; tempX &lt;&lt; ", " &lt;&lt; tempY &lt;&lt; ", 0.0) by " &lt;&lt; angle &lt;&lt; " degrees = "; GLfloat newX = (tempX * cos(angle)) - (tempZ * sin(angle)); GLfloat newY = tempY; GLfloat newZ = (tempX * sin(angle)) - (tempZ * cos(angle)); cout &lt;&lt; "(" &lt;&lt; newX &lt;&lt; ", " &lt;&lt; newY &lt;&lt; ", " &lt;&lt; newZ &lt;&lt; ")\n"; glVertex3d(newX, newY, newZ); } // the following was my old solution, using OpenGL's rotate(), but that // didn't allow me to get back the new point's coordinates. /* glRotatef(angle, 0.0, 1.0, 0.0); // draw a line? if( clickedPoints.size() &gt; 1 ) { glBegin(GL_LINE_STRIP); for(int i=0; i&lt;clickedPoints.size(); i++ ) { glVertex3f((clickedPoints[i].x-250)/250, (clickedPoints[i].y-250)/250, 0.0); } glEnd(); } // everyone gets points glBegin(GL_POINTS); for(int i=0; i&lt;clickedPoints.size(); i++ ) { glVertex3f((clickedPoints[i].x-250)/250, (clickedPoints[i].y-250)/250, 0.0); } glEnd(); */ } glutSwapBuffers(); } </code></pre> <p>EDIT 3: Here is a terrible illustration that illustrates what I need to do. I know the perspective seems off, but what I'm attempting to acquire is the green 'horizontals' in the right subview (this is using the commented out glRotatef() code above):</p> <p><img src="https://i.stack.imgur.com/Qcpno.jpg" alt="Pic"></p> <p><strong>FINAL EDIT</strong> (for future generations!):</p> <p>Here is what I finally got working, after discussing some linear algebra with a teacher at college:</p> <pre><code>void displayPersp(void) { glClear(GL_COLOR_BUFFER_BIT); gluLookAt (-2.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0); glMatrixMode (GL_MODELVIEW); glLoadIdentity (); // draw the axis glBegin(GL_LINES); // x glVertex3f(500.0, 0.0, 0.0); glVertex3f(-500.0, 0.0, 0.0); // y glVertex3f(0.0, -500.0, 0.0); glVertex3f(0.0, 500.0, 0.0); // z glVertex3f(0.0, 0.0, -500.0); glVertex3f(0.0, 0.0, 500.0); glEnd(); cout &lt;&lt; endl; double previousTheta = 0.0; for( int i=0; i&lt;=sweepResolutionMod; i++ ) { double theta = i&gt;0 ? (360/sweepResolutionMod)*i : 0; theta = theta * (M_PI/180); if( clickedPoints.size() &gt; 1 ) { // the 'vertical' piece glBegin(GL_LINE_STRIP); for(int i=0; i&lt;clickedPoints.size(); i++ ) { // normalize GLfloat tempX = (clickedPoints[i].x-250)/250; GLfloat tempY = (clickedPoints[i].y-250)/250; GLfloat tempZ = 0.0; // new points GLfloat newX = ( tempX * cos(theta) ) + ( tempZ * sin(theta) ); GLfloat newY = tempY; GLfloat newZ = ( tempZ * cos(theta) ) - ( tempX * sin(theta) ); glVertex3f(newX, newY, newZ); } glEnd(); // the 'horizontal' piece if( previousTheta != theta ) { glBegin(GL_LINES); for(int i=0; i&lt;clickedPoints.size(); i++ ) { // normalize GLfloat tempX = (clickedPoints[i].x-250)/250; GLfloat tempY = (clickedPoints[i].y-250)/250; GLfloat tempZ = 0.0; // new points GLfloat newX = ( tempX * cos(theta) ) + ( tempZ * sin(theta) ); GLfloat newY = tempY; GLfloat newZ = ( tempZ * cos(theta) ) - ( tempX * sin(theta) ); // previous points GLfloat previousX = ( tempX * cos(previousTheta) ) + ( tempZ * sin(previousTheta) ); GLfloat previousY = tempY; GLfloat previousZ = ( tempZ * cos(previousTheta) ) - ( tempX * sin(previousTheta) ); // horizontal component glVertex3f(newX, newY, newZ); glVertex3f(previousX, previousY, previousZ); } glEnd(); } } previousTheta = theta; } glutSwapBuffers(); } </code></pre>
 

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