Area calculation trapezoid

[dennemark]

Hi,
I have adapted your script to the Rhino3d/Grasshopper environment: https://decodingspaces-toolbox.org/grasshopper-snippets-for-urban-design-and-analysis/

I stumbled over an issue with your algorithm, when performing the minimum cut in a trapezoid. You find the cutting line by linearly interpolating the position on the angled trapezoid edges according to the needed area:

double fraction = areaToCutAway / trapezoidArea; Coordinate pointOfCutOnEdgeA = trapezoidEdgeOnEdgeA.pointAlong(fraction);

As far as I understood, you choose the angled trapezoid edges. But interpolation does not work for them. It is a bit more complicated as seen in this video: https://www.youtube.com/watch?v=GoP6wIR8-DU

I chose to "refractorise" the fraction value according to the video. This is a bit of pseudo code for those who really need to dig into it. Hope it helps.

double distance = distanceOfEdge;
 double wholeDistance = distanceOfEdge+shortestDistanceToIntersectionPointWithOppositeEdge;
 Vector dir = directionOfEdge;
 dir.Unitize();
 double remainingDistance = wholeDistance - distance;
 Vector rotateVec = dir * remainingDistance;
 rotateVec.Rotate(Math.Acos(remainingDistance / wholeDistance), Vector.ZAxis);
 //in the video the first two circles intersect and their intersection point is projected onto the extended edge
 // this can be simply done via Vector dot product
 double projectedDistance = Math.Abs(Vector.DotProduct(rotateVec, dir));
 //afterwards we find calculate the distance of our fraction
 double fractionDistance= fraction * (wholeDistance - projectedDistance);
 // in the video the point of the fraction is projected back onto the big circle. we can use trigonometry for this to create the sides of a triangle
 double adjacentSide = wholeDistance - (fracturedDistance);
 double oppositeSide = Math.Sqrt(Math.Pow(wholeDistance / 2.0, 2) - Math.Pow((wholeDistance / 2.0 - adjacentSide ), 2));
 double hypothenuse = Math.Sqrt(Math.Pow(adjacentSide, 2) + Math.Pow((oppositeSide ), 2));
 //with these values we can calculate the new fraction
 double newFraction = (wholeDistance - hypothenuse) / distance;

 }

Best,
Martin