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    <p>We need to observe some thing before applying any algorithm on captured points.</p> <ol> <li>Generally UIKit does not give the points at equal distance.</li> <li>We need to calculate the intermediate points in between two CGPoints[ Which has captured with Touch moved method]</li> </ol> <p>Now to get smooth line, there are so many ways.</p> <p>Some times we can achieve the by applying second degree polynomial or third degree polynomial or catmullRomSpline algorithms</p> <pre><code>- (float)findDistance:(CGPoint)point lineA:(CGPoint)lineA lineB:(CGPoint)lineB { CGPoint v1 = CGPointMake(lineB.x - lineA.x, lineB.y - lineA.y); CGPoint v2 = CGPointMake(point.x - lineA.x, point.y - lineA.y); float lenV1 = sqrt(v1.x * v1.x + v1.y * v1.y); float lenV2 = sqrt(v2.x * v2.x + v2.y * v2.y); float angle = acos((v1.x * v2.x + v1.y * v2.y) / (lenV1 * lenV2)); return sin(angle) * lenV2; } - (NSArray *)douglasPeucker:(NSArray *)points epsilon:(float)epsilon { int count = [points count]; if(count &lt; 3) { return points; } //Find the point with the maximum distance float dmax = 0; int index = 0; for(int i = 1; i &lt; count - 1; i++) { CGPoint point = [[points objectAtIndex:i] CGPointValue]; CGPoint lineA = [[points objectAtIndex:0] CGPointValue]; CGPoint lineB = [[points objectAtIndex:count - 1] CGPointValue]; float d = [self findDistance:point lineA:lineA lineB:lineB]; if(d &gt; dmax) { index = i; dmax = d; } } //If max distance is greater than epsilon, recursively simplify NSArray *resultList; if(dmax &gt; epsilon) { NSArray *recResults1 = [self douglasPeucker:[points subarrayWithRange:NSMakeRange(0, index + 1)] epsilon:epsilon]; NSArray *recResults2 = [self douglasPeucker:[points subarrayWithRange:NSMakeRange(index, count - index)] epsilon:epsilon]; NSMutableArray *tmpList = [NSMutableArray arrayWithArray:recResults1]; [tmpList removeLastObject]; [tmpList addObjectsFromArray:recResults2]; resultList = tmpList; } else { resultList = [NSArray arrayWithObjects:[points objectAtIndex:0], [points objectAtIndex:count - 1],nil]; } return resultList; } - (NSArray *)catmullRomSplineAlgorithmOnPoints:(NSArray *)points segments:(int)segments { int count = [points count]; if(count &lt; 4) { return points; } float b[segments][4]; { // precompute interpolation parameters float t = 0.0f; float dt = 1.0f/(float)segments; for (int i = 0; i &lt; segments; i++, t+=dt) { float tt = t*t; float ttt = tt * t; b[i][0] = 0.5f * (-ttt + 2.0f*tt - t); b[i][1] = 0.5f * (3.0f*ttt -5.0f*tt +2.0f); b[i][2] = 0.5f * (-3.0f*ttt + 4.0f*tt + t); b[i][3] = 0.5f * (ttt - tt); } } NSMutableArray *resultArray = [NSMutableArray array]; { int i = 0; // first control point [resultArray addObject:[points objectAtIndex:0]]; for (int j = 1; j &lt; segments; j++) { CGPoint pointI = [[points objectAtIndex:i] CGPointValue]; CGPoint pointIp1 = [[points objectAtIndex:(i + 1)] CGPointValue]; CGPoint pointIp2 = [[points objectAtIndex:(i + 2)] CGPointValue]; float px = (b[j][0]+b[j][1])*pointI.x + b[j][2]*pointIp1.x + b[j][3]*pointIp2.x; float py = (b[j][0]+b[j][1])*pointI.y + b[j][2]*pointIp1.y + b[j][3]*pointIp2.y; [resultArray addObject:[NSValue valueWithCGPoint:CGPointMake(px, py)]]; } } for (int i = 1; i &lt; count-2; i++) { // the first interpolated point is always the original control point [resultArray addObject:[points objectAtIndex:i]]; for (int j = 1; j &lt; segments; j++) { CGPoint pointIm1 = [[points objectAtIndex:(i - 1)] CGPointValue]; CGPoint pointI = [[points objectAtIndex:i] CGPointValue]; CGPoint pointIp1 = [[points objectAtIndex:(i + 1)] CGPointValue]; CGPoint pointIp2 = [[points objectAtIndex:(i + 2)] CGPointValue]; float px = b[j][0]*pointIm1.x + b[j][1]*pointI.x + b[j][2]*pointIp1.x + b[j][3]*pointIp2.x; float py = b[j][0]*pointIm1.y + b[j][1]*pointI.y + b[j][2]*pointIp1.y + b[j][3]*pointIp2.y; [resultArray addObject:[NSValue valueWithCGPoint:CGPointMake(px, py)]]; } } { int i = count-2; // second to last control point [resultArray addObject:[points objectAtIndex:i]]; for (int j = 1; j &lt; segments; j++) { CGPoint pointIm1 = [[points objectAtIndex:(i - 1)] CGPointValue]; CGPoint pointI = [[points objectAtIndex:i] CGPointValue]; CGPoint pointIp1 = [[points objectAtIndex:(i + 1)] CGPointValue]; float px = b[j][0]*pointIm1.x + b[j][1]*pointI.x + (b[j][2]+b[j][3])*pointIp1.x; float py = b[j][0]*pointIm1.y + b[j][1]*pointI.y + (b[j][2]+b[j][3])*pointIp1.y; [resultArray addObject:[NSValue valueWithCGPoint:CGPointMake(px, py)]]; } } // the very last interpolated point is the last control point [resultArray addObject:[points objectAtIndex:(count - 1)]]; return resultArray; } </code></pre>
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    1. COVery nice! Could you share some comments on the 2 methods and their parameters?
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