Polygon Area calculation returns negative

[alvpickmans]

Describe the bug
When polygon's vertices are defined clockwise, the area calculation returns negative value.

To Reproduce

using Elements.Geometry;
using NUnit.Framework;
using System.Linq;

namespace Tests
{
    public class Tests
    {

        [Test]
        public void PolygonAreaTest()
        {
            double side = 20;
            Vector3[] vertices = new Vector3[4]
            {
                new Vector3(0,0,0),
                new Vector3(side, 0, 0),
                new Vector3(side, side, 0),
                new Vector3(0, side, 0)
            };

            Polygon ccw = new Polygon(vertices);
            Polygon cw = new Polygon(vertices.Reverse().ToArray());

            double expected = side * side;

            // This passes
            Assert.AreEqual(expected, ccw.Area());

            // This fails
            Assert.AreEqual(expected, cw.Area());
            Assert.IsTrue(ccw.Area() == cw.Area());
        }
    }
}

[anthonyhauck]

Polygon area fix #167 pending review.

[ikeough]

@alvpickmans The fix should be in 0.3.2. Please let us know if it resolves your issue.

[alvpickmans]

@ikeough sadly the unit test above still fails. I think the issue is on the formula that calculates the area, as it assumes a counter-clockwise vertex order(?). A simple fix would be to return the absolute value, but unsure if it will have a side effect somewhere else.
https://github.com/hypar-io/Elements/blob/master/src/Elements/Geometry/Polygon.cs#L596

[ikeough]

That is true. Polygon winding is assumed to be CCW. The simple fix would be nice :), but it would most likely break other area calculations. As "holes" are represented with CW winding. Having the ability to calculate an aggregate area for a perimeter and some holes simply by summing the result of each Area() is nice.

A more elaborate fix would be to provide a method which identifies the winding of a polygon. Then the user can make a determination what to do with the result of the area calculation. I'm guessing that your system uses CW winding for polygons?

[alvpickmans]

I get your point, but I wouldn't agree on having the design/behaviour of a high level class like `Polygon` depending on a particular implementation preference for a lower level class like `Perimeter` or `Floor`. I'm sure it's easier to understand that a perimeter's area is the outer polygon's area minus the sum of the holes than adding an extra method call to define if a polygon is CCW or CW. Besides of the point that a polygon with negative area doesn't make much sense in geometry 😅 In our case, the polygon winding is defined by the user when drawing the polygon geometry, so at the moment we need to always return the absolute value of the area.

[ikeough]

The comment of the Polygon.Area method should indicate that negative values will be returned for CW wound polygons.