floccinaucinihilipilification

Simple basic spiral code implementation 2 with tolerance 0.1

This is the sequel of the previous code implementation of spiral, that time I made a very simple archimedean spiral with the same step over. But sometime, we want more than a step over, a distance between each point of a spiral (tolerance).

Here is my code implementation in c.

 /**********************************************************************  
  *  
  *  
  *    @par    Copyright(C)  
  *    2018     Tokyo University of Agriculture, Saville Lab.  
  *    All rights reserved.  
  *  
  *    @par    History:  
  *    - 2018/07/15    Saville Ramadhona  
  *        - first code.  
  *  
  ***********************************************************************/  
 /*  
  * Program to make spiral curve and put the point on spiral  
  * based on tollerance (point distance).  
  * Not based on parameter of spiral curve.  
  * eg. When tollerance is o.1, distance between adjacent points on spiral   
  * must not exceed the tollerance.   
  *  
  */  
   
   
 #include<stdio.h>  
 #include<math.h>  
   
 #define M_PI 3.14159265358979323846  
   
 /**  
  *    function to evaluate/compute point on spiral  
  *  
  *    @param[in]    param    spiral parameter  
  *    @param[in]    theta    angle in computed point (radians)  
  *    @param[out]    pt        array coordinate of computed point on spiral (x,y)   
  *    @return                radius of center point of spiral to computed point  
  */  
 double evalSpiralpt(double param, double theta, double pt[2])  
 {  
     double r = param*theta;  
     pt[0] = r * cos(theta);  
     pt[1] = r * sin(theta);  
     return r;  
 }  
   
 /**  
  *    function to check distance square between adjacent points  
  *    we do not use sqrt to make computation faster  
  *  
  *    @param[in]    point        newly computed point on spiral   
  *    @param[in]    prevpoint    previously computed point on spiral   
  *    @return                    distance square obetween adjacent points  
  */  
 double checkDistpt2(double point[2], double prevpoint[2])  
 {  
     return (point[0]-prevpoint[0])*(point[0]-prevpoint[0])   
             + (point[1]-prevpoint[1])*(point[1]-prevpoint[1]);  
 }  
   
 //spiral definition r = a + bθ  
 void main()  
 {  
     //remove file if exist  
   int status;  
   status = remove("C:\\Users\\BA17655\\Documents\\spiral.csv");  
     
   //prepare csv file to see the computation result  
   FILE *fp;  
   fp = fopen("C:\\Users\\BA17655\\Documents\\spiral.csv", "a");  
   
   fprintf(fp, "rad, theta, r, x, y, d\n");  
   
     double pi_2 = 2* M_PI;  
     int numTurns = 5;                                      //automatically determine by detecting outer edge, later!  
     double stepover = 0.1;                                 //tool path stepover (USER INPUT)  
     double distanceBetweenTurns = stepover * (1 / (pi_2)); //b  
     double theta = 0.0;                                    //starting angle  
     double offset = 0.0;                                   //a (offset of starting point)  
   
     /*  
     double pointsPerTurn = 20; //to be modified  
     for(int i=0; i<(pointsPerTurn*numTurns+1); i++)  
     {  
         double r = offset + (distanceBetweenTurns*theta);  
         double point[2];  
         point[0] = r * cos(theta);  
         point[1] = r * sin(theta);  
   
         printf("%f %f %f %f \n", theta*(180.0/M_PI), r, point[0], point[1]);  
         theta += pi_2 / pointsPerTurn;  
     }  
     */  
   
     double dist_thres2 = 0.01;          //distance threshold(control point tollerance - USER INPUT)  
     int cnt = 0;  
     double point[2];                    //x, y coordinate control point on spiral  
     double prevpoint[2];  
     double prevtheta;  
     double degree;  
     double sizelimit = numTurns * 360.0; //to sizelimit the size of spiral  
     do  
     {  
         //evaluate point in spiral   
         double r = evalSpiralpt(distanceBetweenTurns, theta, point);  
   
         if( cnt < 1 )  
         {  
             fprintf(fp, "%f, %f, %f, %f, %f\n", theta, theta*(180.0/M_PI), r, point[0], point[1]);  
             theta += pi_2 * dist_thres2;  
         }  
         if( cnt > 0 )  
         {  
             //check distance of control point  
             double dist2 = checkDistpt2(point, prevpoint);  
   
             //check if point distance exceed tolerance  
             if( dist2 > dist_thres2 )   
             { //if exeec tollerance, compute new control point  
                 do   
                 {  
                     //make the new point to be located in the middle of previous and current point  
                     theta = (theta + prevtheta) * 0.5;  
                     r = evalSpiralpt(distanceBetweenTurns, theta, point);  
                     dist2 = checkDistpt2(point, prevpoint);  
   
                     //when above is not enough, do it one more time!  
                     if( dist2 > dist_thres2 )  
                     {  
                         theta = (theta + prevtheta) * 0.5;  
                         r = evalSpiralpt(distanceBetweenTurns, theta, point);  
                         dist2 = checkDistpt2(point, prevpoint);  
                     }  
                 }while( dist2 > dist_thres2 ); //when point distance lies under the tollerance, exit loop  
             }  
   
             fprintf(fp, "%f, %f, %f, %f, %f, %f\n", theta, theta*(180.0/M_PI), r, point[0], point[1], dist2);  
             prevtheta = theta;  
             theta += pi_2 * dist_thres2;  
         }          
           
         cnt++;  
                   
         prevpoint[0] = point[0];  
         prevpoint[1] = point[1];  
         degree = theta*(180.0/M_PI);  
   
     }while( degree <= sizelimit );  
   
 }

After running the code, it will print out the angle (radian), angle (degree), r of each point(interpreted as 1/curvature), x, y coordinate of each point, and the distance of each point.
The plotted spiral from the code in excel is as shown below.

Pretty simple right!

spiral 2

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