public void Test_S1ChordAngle_Trigonometry()
{
const int kIters = 20;
for (int iter = 0; iter <= kIters; ++iter)
{
double radians = Math.PI * iter / kIters;
S1ChordAngle angle = new(S1Angle.FromRadians(radians));
Assert2.Near(Math.Sin(radians), angle.Sin(), S2.DoubleError);
Assert2.Near(Math.Cos(radians), angle.Cos(), S2.DoubleError);
// Since the tan(x) is unbounded near Pi/4, we map the result back to an
// angle before comparing. (The assertion is that the result is equal to
// the tangent of a nearby angle.)
Assert2.Near(Math.Atan(Math.Tan(radians)), Math.Atan(angle.Tan()), S2.DoubleError);
}
// Unlike S1Angle, S1ChordAngle can represent 90 and 180 degrees exactly.
S1ChordAngle angle90 = S1ChordAngle.FromLength2(2);
S1ChordAngle angle180 = S1ChordAngle.FromLength2(4);
Assert.Equal(1, angle90.Sin());
Assert.Equal(0, angle90.Cos());
Assert.Equal(double.PositiveInfinity, angle90.Tan());
Assert.Equal(0, angle180.Sin());
Assert.Equal(-1, angle180.Cos());
Assert.Equal(0, angle180.Tan());
}
// Faster than the function above, but cannot accurately represent distances
// near 180 degrees due to the limitations of S1ChordAngle.
public static S2Point GetPointOnRay(S2Point origin, S2Point dir, S1ChordAngle r)
{
System.Diagnostics.Debug.Assert(origin.IsUnitLength());
System.Diagnostics.Debug.Assert(dir.IsUnitLength());
// The error bound below includes the error in computing the dot product.
System.Diagnostics.Debug.Assert(origin.DotProd(dir) <=
S2.kRobustCrossProdError + 0.75 * S2.DoubleEpsilon);
// Mathematically the result should already be unit length, but we normalize
// it anyway to ensure that the error is within acceptable bounds.
// (Otherwise errors can build up when the result of one interpolation is
// fed into another interpolation.)
//
// Note that it is much cheaper to compute the sine and cosine of an
// S1ChordAngle than an S1Angle.
return((r.Cos() * origin + r.Sin() * dir).Normalize());
}
