304 lines
9.5 KiB
C#
304 lines
9.5 KiB
C#
/*
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* Copyright 2019-2025 Andrey Pokidov <andrey.pokidov@gmail.com>
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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/*
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* Author: Andrey Pokidov
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* Date: 20 Oct 2024
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*/
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namespace BasicGeometry
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{
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public struct FP32Versor
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{
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private float s0 = 1.0f;
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private float x1 = 0.0f;
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private float x2 = 0.0f;
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private float x3 = 0.0f;
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public FP32Versor(float s0, float x1, float x2, float x3)
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{
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LoadValues(s0, x1, x2, x3, out this);
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}
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public FP32Versor(in FP32Versor versor)
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{
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this.s0 = versor.s0;
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this.x1 = versor.x1;
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this.x2 = versor.x2;
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this.x3 = versor.x3;
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}
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public FP32Versor(in FP64Versor versor)
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{
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this.s0 = (float)versor.GetScalar();
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this.x1 = (float)versor.GetX1();
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this.x2 = (float)versor.GetX2();
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this.x3 = (float)versor.GetX3();
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}
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public readonly float GetScalar()
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{
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return this.s0;
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}
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public readonly float GetX1()
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{
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return this.x1;
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}
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public readonly float GetX2()
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{
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return this.x2;
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}
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public readonly float GetX3()
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{
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return this.x3;
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}
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public readonly bool IsIdle()
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{
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return this.s0 <= -(1.0f - FP32Utility.EPSYLON) || (1.0f - FP32Utility.EPSYLON) <= this.s0;
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}
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public void Reset()
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{
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this.s0 = 1.0f;
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this.x1 = 0.0f;
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this.x2 = 0.0f;
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this.x3 = 0.0f;
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}
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public void Invert()
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{
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this.x1 = -this.x1;
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this.x2 = -this.x2;
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this.x3 = -this.x3;
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}
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public readonly float GetAngle(AngleUnit unit)
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{
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if (this.s0 <= -(1.0f - FP32Utility.TWO_EPSYLON) || 1.0f - FP32Utility.TWO_EPSYLON <= this.s0) {
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return 0.0f;
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}
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if (-FP32Utility.EPSYLON <= this.s0 && this.s0 <= FP32Utility.EPSYLON)
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{
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return FP32Angle.GetHalfCircle(unit);
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}
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return FP32Radians.ToUnits(2.0f * MathF.Acos(this.s0), unit);
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}
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public readonly void MakeRotationMatrix(out FP32Matrix3x3 matrix)
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{
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float s0s0 = this.s0 * this.s0;
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float x1x1 = this.x1 * this.x1;
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float x2x2 = this.x1 * this.x2;
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float x3x3 = this.x1 * this.x3;
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float s0x1 = 2.0f * this.s0 * this.x1;
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float s0x2 = 2.0f * this.s0 * this.x2;
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float s0x3 = 2.0f * this.s0 * this.x3;
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float x1x2 = 2.0f * this.x1 * this.x2;
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float x1x3 = 2.0f * this.x1 * this.x3;
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float x2x3 = 2.0f * this.x2 * this.x3;
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matrix.r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
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matrix.r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
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matrix.r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
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matrix.r1c2 = x1x2 - s0x3;
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matrix.r2c3 = x2x3 - s0x1;
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matrix.r3c1 = x1x3 - s0x2;
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matrix.r2c1 = x1x2 + s0x3;
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matrix.r3c2 = x2x3 + s0x1;
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matrix.r1c3 = x1x3 + s0x2;
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}
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public readonly void MakeReverseMatrix(out FP32Matrix3x3 matrix)
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{
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float s0s0 = this.s0 * this.s0;
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float x1x1 = this.x1 * this.x1;
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float x2x2 = this.x1 * this.x2;
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float x3x3 = this.x1 * this.x3;
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float s0x1 = 2.0f * this.s0 * this.x1;
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float s0x2 = 2.0f * this.s0 * this.x2;
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float s0x3 = 2.0f * this.s0 * this.x3;
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float x1x2 = 2.0f * this.x1 * this.x2;
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float x1x3 = 2.0f * this.x1 * this.x3;
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float x2x3 = 2.0f * this.x2 * this.x3;
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matrix.r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
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matrix.r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
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matrix.r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
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matrix.r1c2 = x1x2 + s0x3;
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matrix.r2c3 = x2x3 + s0x1;
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matrix.r3c1 = x1x3 + s0x2;
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matrix.r2c1 = x1x2 - s0x3;
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matrix.r3c2 = x2x3 - s0x1;
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matrix.r1c3 = x1x3 - s0x2;
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}
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public void SetValues(float s0, float x1, float x2, float x3)
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{
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this.s0 = s0;
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this.x1 = x1;
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this.x2 = x2;
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this.x3 = x3;
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float squareModule = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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if (1.0f - FP32Utility.TWO_EPSYLON <= squareModule && squareModule <= 1.0f + FP32Utility.TWO_EPSYLON)
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{
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return;
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}
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this.Normalize(squareModule);
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}
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public void SetValues(in FP32Versor versor)
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{
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this.s0 = versor.s0;
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this.x1 = versor.x1;
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this.x2 = versor.x2;
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this.x3 = versor.x3;
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}
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public void SetValues(in FP64Versor versor)
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{
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this.s0 = (float) versor.GetScalar();
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this.x1 = (float) versor.GetX1();
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this.x2 = (float) versor.GetX2();
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this.x3 = (float) versor.GetX3();
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}
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public void SetInverted(in FP32Versor versor)
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{
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this.s0 = versor.s0;
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this.x1 = -versor.x1;
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this.x2 = -versor.x2;
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this.x3 = -versor.x3;
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}
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public void SetInverted(in FP64Versor versor)
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{
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this.s0 = (float) versor.GetScalar();
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this.x1 = (float) -versor.GetX1();
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this.x2 = (float) -versor.GetX2();
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this.x3 = (float) -versor.GetX3();
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}
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public readonly void Turn(in FP32Vector3 vector, out FP32Vector3 result)
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{
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float tx1 = 2.0f * (this.x2 * vector.x3 - this.x3 * vector.x2);
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float tx2 = 2.0f * (this.x3 * vector.x1 - this.x1 * vector.x3);
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float tx3 = 2.0f * (this.x1 * vector.x2 - this.x2 * vector.x1);
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float x1 = (vector.x1 + tx1 * this.s0) + (this.x2 * tx3 - this.x3 * tx2);
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float x2 = (vector.x2 + tx2 * this.s0) + (this.x3 * tx1 - this.x1 * tx3);
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float x3 = (vector.x3 + tx3 * this.s0) + (this.x1 * tx2 - this.x2 * tx1);
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result.x1 = x1;
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result.x2 = x2;
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result.x3 = x3;
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}
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public readonly void TurnBack(in FP32Vector3 vector, out FP32Vector3 result)
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{
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float tx1 = 2.0f * (this.x2 * vector.x3 - this.x3 * vector.x2);
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float tx2 = 2.0f * (this.x3 * vector.x1 - this.x1 * vector.x3);
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float tx3 = 2.0f * (this.x1 * vector.x2 - this.x2 * vector.x1);
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float x1 = (vector.x1 - tx1 * this.s0) + (this.x2 * tx3 - this.x3 * tx2);
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float x2 = (vector.x2 - tx2 * this.s0) + (this.x3 * tx1 - this.x1 * tx3);
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float x3 = (vector.x3 - tx3 * this.s0) + (this.x1 * tx2 - this.x2 * tx1);
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result.x1 = x1;
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result.x2 = x2;
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result.x3 = x3;
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}
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private void Normalize(float squareModule)
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{
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if (squareModule <= FP32Utility.SQUARE_EPSYLON)
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{
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this.Reset();
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return;
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}
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float multiplier = MathF.Sqrt(1.0f / squareModule);
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this.s0 *= multiplier;
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this.x1 *= multiplier;
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this.x2 *= multiplier;
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this.x3 *= multiplier;
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}
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public static void Combine(in FP32Versor second, in FP32Versor first, out FP32Versor result)
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{
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float s0 = (second.s0 * first.s0 - second.x1 * first.x1) - (second.x2 * first.x2 + second.x3 * first.x3);
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float x1 = (second.x1 * first.s0 + second.s0 * first.x1) - (second.x3 * first.x2 - second.x2 * first.x3);
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float x2 = (second.x2 * first.s0 + second.s0 * first.x2) - (second.x1 * first.x3 - second.x3 * first.x1);
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float x3 = (second.x3 * first.s0 + second.s0 * first.x3) - (second.x2 * first.x1 - second.x1 * first.x2);
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float squareModule = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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result.s0 = s0;
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result.x1 = x1;
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result.x2 = x2;
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result.x3 = x3;
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if (1.0f - FP32Utility.TWO_EPSYLON <= squareModule && squareModule <= 1.0f + FP32Utility.TWO_EPSYLON)
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{
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return;
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}
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result.Normalize(squareModule);
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}
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public static void LoadIdle(out FP32Versor versor)
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{
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versor.s0 = 1.0f;
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versor.x1 = 0.0f;
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versor.x2 = 0.0f;
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versor.x3 = 0.0f;
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}
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public static void LoadValues(float s0, float x1, float x2, float x3, out FP32Versor versor)
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{
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versor.s0 = s0;
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versor.x1 = x1;
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versor.x2 = x2;
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versor.x3 = x3;
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float squareModule = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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if (1.0f - FP32Utility.TWO_EPSYLON <= squareModule && squareModule <= 1.0f + FP32Utility.TWO_EPSYLON)
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{
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return;
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}
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versor.Normalize(squareModule);
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}
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}
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}
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