bgc-net/BasicGeometry/QuaternionFP64.cs

using System;

namespace BasicGeometry
{
    public struct QuaternionFP64
    {
        public double s0 = 0.0, x1 = 0.0, x2 = 0.0, x3 = 0.0;

        public QuaternionFP64(double s0, double x1, double x2, double x3)
        {
            this.s0 = s0;
            this.x1 = x1;
            this.x2 = x2;
            this.x3 = x3;
        }

        public QuaternionFP64(in QuaternionFP32 quaternion)
        {
            this.s0 = quaternion.s0;
            this.x1 = quaternion.x1;
            this.x2 = quaternion.x2;
            this.x3 = quaternion.x3;
        }

        public QuaternionFP64(in QuaternionFP64 quaternion)
        {
            this.s0 = quaternion.s0;
            this.x1 = quaternion.x1;
            this.x2 = quaternion.x2;
            this.x3 = quaternion.x3;
        }

        public readonly double GetSquareModulus()
        {
            return this.s0 * this.s0 + this.x1 * this.x1 + (this.x2 * this.x2 + this.x3 * this.x3);
        }

        public readonly double GetModulus()
        {
            return Math.Sqrt(this.GetSquareModulus());
        }

        public readonly bool IsZero()
        {
            return this.GetSquareModulus() <= UtilityFP64.SQUARE_EPSYLON;
        }

        public readonly bool IsUnit()
        {
            return UtilityFP64.IsSqareUnit(this.GetSquareModulus());
        }

        public void Reset()
        {
            this.s0 = 0.0;
            this.x1 = 0.0;
            this.x2 = 0.0;
            this.x3 = 0.0;
        }

        public void SetToIdentity()
        {
            this.s0 = 1.0;
            this.x1 = 0.0;
            this.x2 = 0.0;
            this.x3 = 0.0;
        }

        public void Conjugate()
        {
            this.x1 = -this.x1;
            this.x2 = -this.x2;
            this.x3 = -this.x3;
        }

        public void SetValues(double s0, double x1, double x2, double x3)
        {
            this.s0 = s0;
            this.x1 = x1;
            this.x2 = x2;
            this.x3 = x3;
        }

        public void Set(in QuaternionFP32 quaternion)
        {
            this.s0 = quaternion.s0;
            this.x1 = quaternion.x1;
            this.x2 = quaternion.x2;
            this.x3 = quaternion.x3;
        }

        public void Set(in QuaternionFP64 quaternion)
        {
            this.s0 = quaternion.s0;
            this.x1 = quaternion.x1;
            this.x2 = quaternion.x2;
            this.x3 = quaternion.x3;
        }

        public static void MakeConjugate(in QuaternionFP64 quaternion, out QuaternionFP64 conjugate)
        {
            conjugate.s0 = quaternion.s0;
            conjugate.x1 = -quaternion.x1;
            conjugate.x2 = -quaternion.x2;
            conjugate.x3 = -quaternion.x3;
        }

        public readonly void MakeRotationMatrix(out Matrix3x3FP64 matrix)
        {
            double s0s0 = this.s0 * this.s0;
            double x1x1 = this.x1 * this.x1;
            double x2x2 = this.x2 * this.x2;
            double x3x3 = this.x3 * this.x3;

            double squareModulus = (s0s0 + x1x1) + (x2x2 + x3x3);

            if (squareModulus <= UtilityFP64.SQUARE_EPSYLON || !double.IsFinite(squareModulus))
            {
                Matrix3x3FP64.LoadIdentity(out matrix);
                return;
            }

            double corrector1 = 1.0 / squareModulus;

            double s0x1 = this.s0 * this.x1;
            double s0x2 = this.s0 * this.x2;
            double s0x3 = this.s0 * this.x3;
            double x1x2 = this.x1 * this.x2;
            double x1x3 = this.x1 * this.x3;
            double x2x3 = this.x2 * this.x3;

            double corrector2 = 2.0 * corrector1;

            matrix.r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
            matrix.r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
            matrix.r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

            matrix.r1c2 = corrector2 * (x1x2 - s0x3);
            matrix.r2c3 = corrector2 * (x2x3 - s0x1);
            matrix.r3c1 = corrector2 * (x1x3 - s0x2);

            matrix.r2c1 = corrector2 * (x1x2 + s0x3);
            matrix.r3c2 = corrector2 * (x2x3 + s0x1);
            matrix.r1c3 = corrector2 * (x1x3 + s0x2);
        }

        public readonly void MakeReverseMatrix(out Matrix3x3FP64 matrix)
        {
            double s0s0 = this.s0 * this.s0;
            double x1x1 = this.x1 * this.x1;
            double x2x2 = this.x2 * this.x2;
            double x3x3 = this.x3 * this.x3;

            double squareModulus = (s0s0 + x1x1) + (x2x2 + x3x3);

            if (squareModulus <= UtilityFP64.SQUARE_EPSYLON || !double.IsFinite(squareModulus))
            {
                Matrix3x3FP64.LoadIdentity(out matrix);
                return;
            }

            double corrector1 = 1.0 / squareModulus;

            double s0x1 = this.s0 * this.x1;
            double s0x2 = this.s0 * this.x2;
            double s0x3 = this.s0 * this.x3;
            double x1x2 = this.x1 * this.x2;
            double x1x3 = this.x1 * this.x3;
            double x2x3 = this.x2 * this.x3;

            double corrector2 = 2.0 * corrector1;

            matrix.r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
            matrix.r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
            matrix.r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

            matrix.r1c2 = corrector2 * (x1x2 + s0x3);
            matrix.r2c3 = corrector2 * (x2x3 + s0x1);
            matrix.r3c1 = corrector2 * (x1x3 + s0x2);

            matrix.r2c1 = corrector2 * (x1x2 - s0x3);
            matrix.r3c2 = corrector2 * (x2x3 - s0x1);
            matrix.r1c3 = corrector2 * (x1x3 - s0x2);
        }

        public static void Add(in QuaternionFP64 quaternion1, in QuaternionFP64 quaternion2, out QuaternionFP64 sum)
        {
            sum.s0 = quaternion1.s0 + quaternion2.s0;
            sum.x1 = quaternion1.x1 + quaternion2.x1;
            sum.x2 = quaternion1.x2 + quaternion2.x2;
            sum.x3 = quaternion1.x3 + quaternion2.x3;
        }

        public static void Subtract(in QuaternionFP64 minuend, in QuaternionFP64 subtrahend, out QuaternionFP64 difference)
        {
            difference.s0 = minuend.s0 - subtrahend.s0;
            difference.x1 = minuend.x1 - subtrahend.x1;
            difference.x2 = minuend.x2 - subtrahend.x2;
            difference.x3 = minuend.x3 - subtrahend.x3;
        }

        public static void Multiply(in QuaternionFP64 left, in QuaternionFP64 right, out QuaternionFP64 product)
        {
            double s0 = left.s0 * right.s0 - left.x1 * right.x1 - (left.x2 * right.x2 + left.x3 * right.x3);
            double x1 = left.x1 * right.s0 + left.s0 * right.x1 - (left.x3 * right.x2 - left.x2 * right.x3);
            double x2 = left.x2 * right.s0 + left.s0 * right.x2 - (left.x1 * right.x3 - left.x3 * right.x1);
            double x3 = left.x3 * right.s0 + left.s0 * right.x3 - (left.x2 * right.x1 - left.x1 * right.x2);

            product.s0 = s0;
            product.x1 = x1;
            product.x2 = x2;
            product.x3 = x3;
        }

        public static bool AreClose(QuaternionFP32 quaternion1, QuaternionFP32 quaternion2)
        {
            double ds0 = quaternion1.s0 - quaternion2.s0;
            double dx1 = quaternion1.x1 - quaternion2.x1;
            double dx2 = quaternion1.x2 - quaternion2.x2;
            double dx3 = quaternion1.x3 - quaternion2.x3;

            double squareModulus1 = quaternion1.GetSquareModulus();
            double squareModulus2 = quaternion2.GetSquareModulus();
            double squareDistance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);

            if (squareModulus1 <= UtilityFP64.EPSYLON_EFFECTIVENESS_LIMIT || squareModulus2 <= UtilityFP64.EPSYLON_EFFECTIVENESS_LIMIT) {
                return squareDistance <= UtilityFP64.SQUARE_EPSYLON;
            }

            return squareDistance <= UtilityFP64.SQUARE_EPSYLON * squareModulus1 && squareDistance <= UtilityFP64.SQUARE_EPSYLON * squareModulus2;
        }
    }
}