Method segmentSolveTimeForDistance

src/cinder/Path2d.cpp:2141–2178

}

float Path2d::segmentSolveTimeForDistance( size_t segment, float segmentLength, float segmentRelativeDistance, float tolerance, int maxIterations ) const
{
	// initialize bisection endpoints
	float a = 0, b = 1;
	float p = segmentRelativeDistance / segmentLength;    // make first guess

	// we want to calculate a value 'p' such that segmentLength( mCurrentSegment, mCurrentT, mCurrentT + p ) == lengthIncrement

	// iterate and look for zeros
	float lastArcLength = 0;
	float currentT = 0;
	for( int i = 0; i < maxIterations; ++i ) {
		// compute function value and test against zero
		lastArcLength = calcSegmentLength( segment, currentT, currentT + p );
		float delta = lastArcLength - segmentRelativeDistance;
		if( math<float>::abs( delta ) < tolerance ) {
			break;
		}

		 // update bisection endpoints
		if( delta < 0 )
			a = p;
		else
			b = p;

		// get speed along curve
		const float speed = length( getSegmentTangent( segment, currentT + p ) );

		// if result will lie outside [a,b]
		if( ((p-a)*speed - delta)*((p-b)*speed - delta) > -tolerance )
			p = 0.5f*(a+b);	// do bisection
		else
			p -= delta/speed; // otherwise Newton-Raphson
	}
	// If we failed to converge, hopefully 'p' is close enough

	return ( p + segment ) / (float)mSegments.size();
}

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Path2dCalcCache