Trapezoidal Teacups -- Geometry Test (Problem) -- 12-09-2015
Phil Weinstein, CADSWES ... go to fixed

// returns success indication
bool TeacupGfxItem::computeTrapezoidValueDims (
             TcupGeom geom,                // Input
             double pix2PerUnitVal,        // Input, square pixel per unit val
             double value,                 // Input
             double& retValueHeight,       // Returned
             double& retValueWidth) const  // Returned

... ... ...
... ... ...

   // **********************************
   // ***  (1) Compute Value Height  ***
   // **********************************

   // All measurements are made with respect to the "Reference" trapezoid.
   // Both the "Reference" and "Value" trapeziods have the same botWid.
   //
   // KNOWN:
   //   Reference Trapezoid: maxTopWid, botWid, refHgt
   //   Value Trapezoid: botWid, valArea
   //
   // SOLVE FOR:
   //   Value Trapezoid: valHgt (retValueHeight)
   //
   // Equation 1 (trapezoid):
   //   valArea == 0.5 * (valTopWid + botWid) * valHgt
   //   2 * valArea == (valTopWid + botWid) * valHgt
   //
   // Equation 2 (congruent):
   //   (valTopWid / valHgt) == (maxTopWid / refHgt)
   //   valTopWid == valHgt * (maxTopWId / refHgt)
   //
   // Combined Equations, Format as Quadratic Equation
   //  2 * valArea == ((valHgt * (maxTopWid / refHgt)) + botWid) * valHgt
   //  2 * valArea == (valHgt^2 * (maxTopWid / refHgt)) + (valHgt * botWid)
   //  0 == ((maxTopWid/refHgt) * valHgt^2) + (botWid*valHgt) + (-2*valArea)
   //
   // Apply Quadratic Forumla
   //   a == maxTopWid/refHgt
   //   b == botWid
   //   c == (-2 * valArea)
   //   x == -b +- sqrt (b^2 - 4ac) / 2a

   const double a = maxTopWid / refHgt;
   const double b = botWid;
   const double c = (-2.0 * valArea);

   const double squareTerm = (b * b) - (4.0 * a * c);
   if (squareTerm < 0.0)
      return (false); //----->>

   const double rootTerm = sqrt (squareTerm);
   const double x1 = (-b - rootTerm) / (2.0 * a);
   const double x2 = (-b + rootTerm) / (2.0 * a);

   retValueHeight = std::max (x1, x2);

   // *********************************
   // ***  (2) Compute Value Width  ***
   // *********************************

   retValueWidth = (retValueHeight * (maxTopWid - botWid) / refHgt) + botWid;

   // std::cout << mname << " [#" << callCnt << "]"
   //           << " val "      << value
   //           << ", valArea " << valArea
   //           << ", p2perV "  << pix2PerUnitVal
   //           << ", refHgt "  << refHgt
   //           << ", hgt1 "    << x1
   //           << ", hgt2 "    << x2
   //           << ", botWid "  << botWid
   //           << ", topWid "  << maxTopWid
   //           << ", wid "     << retValueWidth
   //           << std::endl;

   return true;
}