Trapezoidal Teacups -- Geometry Test (Corrected) -- 12-10-2015
Phil Weinstein, CADSWES ... go to problem

// 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

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

   // ********************************
   // ***  Geometric Computations  ***
   // ********************************

   //----------------------------------------------------------------------
   // UNITS: pixels and square-pixels.
   //
   // KNOWN: [H3] refHgt    -- reference trapezoid height
   // KNOWN: [L3] maxTopWid -- reference trapezoid top width
   // KNOWN: [L1] botWid    -- trapezoid bottom width (both trapezoids)
   // KNOWN: [V3] cupArea   -- reference trapezoid area
   // KNOWN: [V1] valArea   -- value trapezoid area
   //
   // SOLVE FOR: [H1] retValueHeight -- value trapezoid height
   // SOLVE FOR: [L2] retValueWidth  -- value trapezoid top width
   //
   //
   //       +----------- L3 -----------+   ----   ----
   //        +                        +     |      |
   //         +         [V2]         +      H2     |
   //          +                    +       |      |
   //           +------- L2 -------+       ----    H3
   //            +                +         |      |
   //             +     [V1]     +          H1     |
   //              +            +           |      |
   //               +--- L1 ---+           ----   ----
   //
   //               V3 == V1 + V2
   //
   //----------------------------------------------------------------------

   const double H3 = refHgt;
   const double L3 = maxTopWid;
   const double L1 = botWid;
   const double V1 = valArea;

   if (fabs (H3) < NEGL)
      return (false); //----->>

   const double L2_squared = (2.0 * V1 * (L3 - L1) / H3) + (L1 * L1);

   // Note: It's reasonable to clip L2 to zero in the case of L2_squared
   // being negative. This occurs in the case of an "inverted" trapezoid
   // cup (with the top narrower than the bottom), and the "current" value
   // overflowing the maximum value.

   double L2 (0.0);
   static int overflowCnt (0);
   if (L2_squared < 0.0)
      ++overflowCnt; // diag breakpoint
   else
      L2 = sqrt (L2_squared);

   if (fabs (L1 + L2) < NEGL)
      return (false); //----->>

   const double H1 = (2.0 * V1) / (L1 + L2);

   retValueHeight = H1;
   retValueWidth = L2;

   return (true);
}