angle_increment_using_max_deviation()

static double angle_increment_using_max_deviation ( double  max_deviation, double  radius  )

static

Definition at line 155 of file lwstroke.c.

{
        double increment, halfAngle, maxErr;
        if ( max_deviation <= 0 )
        {
                lwerror("lwarc_linearize: max deviation must be bigger than 0, got %.15g", max_deviation);
                return -1;
        }
 
        /*
         * Ref: https://en.wikipedia.org/wiki/Sagitta_(geometry)
         *
         * An arc "sagitta" (distance between middle point of arc and
         * middle point of corresponding chord) is defined as:
         *
         *   sagitta = radius * ( 1 - cos( angle ) );
         *
         * We want our sagitta to be at most "tolerance" long,
         * and we want to find out angle, so we use the inverse
         * formula:
         *
         *   tol = radius * ( 1 - cos( angle ) );
         *   1 - cos( angle ) =  tol/radius
         *   - cos( angle ) =  tol/radius - 1
         *   cos( angle ) =  - tol/radius + 1
         *   angle = acos( 1 - tol/radius )
         *
         * Constraints: 1.0 - tol/radius must be between -1 and 1
         * which means tol must be between 0 and 2 times
         * the radius, which makes sense as you cannot have a
         * sagitta bigger than twice the radius!
         *
         */
        maxErr = max_deviation;
        if ( maxErr > radius * 2 )
        {
                maxErr = radius * 2;
                LWDEBUGF(2,
                         "lwarc_linearize: tolerance %g is too big, "
                         "using arc-max 2 * radius == %g",
                         max_deviation,
                         maxErr);
        }
        do {
                halfAngle = acos( 1.0 - maxErr / radius );
                /* TODO: avoid a loop here, going rather straight to
                 *       a minimum angle value */
                if ( halfAngle != 0 ) break;
                LWDEBUGF(2, "lwarc_linearize: tolerance %g is too small for this arc"
                                                                " to compute approximation angle, doubling it", maxErr);
                maxErr *= 2;
        } while(1);
        increment = 2 * halfAngle;
        LWDEBUGF(2,
                 "lwarc_linearize: maxDiff:%g, radius:%g, halfAngle:%g, increment:%g (%g degrees)",
                 max_deviation,
                 radius,
                 halfAngle,
                 increment,
                 increment * 180 / M_PI);
 
        return increment;
}

References LWDEBUGF, and lwerror().

Referenced by lwarc_linearize().

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