366 lines
12 KiB
C#
366 lines
12 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 Geometry
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{
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public struct SPVersor
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{
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public static readonly SPVersor IDLE = new SPVersor(1.0f, 0.0f, 0.0f, 0.0f, 1.0f);
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private float s0;
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private float x1;
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private float x2;
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private float x3;
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private float corrector;
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private SPVersor(float s0, float x1, float x2, float x3, float corrector)
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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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this.corrector = corrector;
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}
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public SPVersor()
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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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this.corrector = 1.0f;
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}
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public SPVersor(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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this.corrector = 2.0f - squareModule;
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if (squareModule < 1.0f - SPUtility.TWO_EPSYLON || 1.0f + SPUtility.TWO_EPSYLON < squareModule)
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{
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this.Normalize(squareModule);
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}
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else if (s0 < -1.0f + SPUtility.EPSYLON || 1.0f - SPUtility.EPSYLON < s0)
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{
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this.Reset();
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}
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}
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public SPVersor(in SPVersor 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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this.corrector = versor.corrector;
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}
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public SPVersor(in DPVersor 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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float squareModule = (this.s0 * this.s0 + this.x1 * this.x1) + (this.x2 * this.x2 + this.x3 * this.x3);
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this.corrector = 2.0f - squareModule;
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if (squareModule < 1.0f - SPUtility.TWO_EPSYLON || 1.0f + SPUtility.TWO_EPSYLON < squareModule)
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{
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this.Normalize(squareModule);
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}
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else if (s0 < -1.0f + SPUtility.EPSYLON || 1.0f - SPUtility.EPSYLON < s0)
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{
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this.Reset();
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}
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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 float GetCorrector()
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{
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return this.corrector;
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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 - SPUtility.EPSYLON) || (1.0f - SPUtility.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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this.corrector = 1.0f;
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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 - SPUtility.TWO_EPSYLON) || 1.0f - SPUtility.TWO_EPSYLON <= this.s0) {
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return 0.0f;
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}
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if (-SPUtility.EPSYLON <= this.s0 && this.s0 <= SPUtility.EPSYLON)
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{
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return SPAngle.GetHalfCircle(unit);
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}
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return SPAngle.ConvertFromRadians(2.0f * MathF.Acos(s0), unit);
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}
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public readonly void MakeRotationMatrix(out SPMatrix3x3 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 = this.s0 * this.x1;
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float s0x2 = this.s0 * this.x2;
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float s0x3 = this.s0 * this.x3;
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float x1x2 = this.x1 * this.x2;
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float x1x3 = this.x1 * this.x3;
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float x2x3 = this.x2 * this.x3;
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float corrector2 = 2.0f * this.corrector;
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matrix.r1c1 = this.corrector * ((s0s0 + x1x1) - (x2x2 + x3x3));
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matrix.r2c2 = this.corrector * ((s0s0 + x2x2) - (x1x1 + x3x3));
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matrix.r3c3 = this.corrector * ((s0s0 + x3x3) - (x1x1 + x2x2));
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matrix.r1c2 = corrector2 * (x1x2 - s0x3);
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matrix.r2c3 = corrector2 * (x2x3 - s0x1);
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matrix.r3c1 = corrector2 * (x1x3 - s0x2);
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matrix.r2c1 = corrector2 * (x1x2 + s0x3);
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matrix.r3c2 = corrector2 * (x2x3 + s0x1);
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matrix.r1c3 = corrector2 * (x1x3 + s0x2);
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}
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public readonly void MakeReverseMatrix(out SPMatrix3x3 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 = this.s0 * this.x1;
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float s0x2 = this.s0 * this.x2;
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float s0x3 = this.s0 * this.x3;
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float x1x2 = this.x1 * this.x2;
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float x1x3 = this.x1 * this.x3;
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float x2x3 = this.x2 * this.x3;
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float corrector2 = 2.0f * this.corrector;
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matrix.r1c1 = this.corrector * ((s0s0 + x1x1) - (x2x2 + x3x3));
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matrix.r2c2 = this.corrector * ((s0s0 + x2x2) - (x1x1 + x3x3));
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matrix.r3c3 = this.corrector * ((s0s0 + x3x3) - (x1x1 + x2x2));
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matrix.r1c2 = corrector2 * (x1x2 + s0x3);
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matrix.r2c3 = corrector2 * (x2x3 + s0x1);
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matrix.r3c1 = corrector2 * (x1x3 + s0x2);
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matrix.r2c1 = corrector2 * (x1x2 - s0x3);
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matrix.r3c2 = corrector2 * (x2x3 - s0x1);
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matrix.r1c3 = corrector2 * (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 (squareModule < 1.0f - SPUtility.TWO_EPSYLON || 1.0f + SPUtility.TWO_EPSYLON < squareModule)
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{
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this.Normalize(squareModule);
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return;
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}
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if (s0 < -1.0f + SPUtility.EPSYLON || 1.0f - SPUtility.EPSYLON < s0) {
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this.Reset();
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return;
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}
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this.corrector = 2.0f - squareModule;
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}
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public void SetValues(in SPVersor 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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this.corrector = versor.corrector;
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}
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public void SetValues(in DPVersor versor)
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{
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this.SetValues(
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(float)versor.GetScalar(),
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(float)versor.GetX1(),
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(float)versor.GetX2(),
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(float)versor.GetX3()
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);
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}
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public void SetInverted(in SPVersor 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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this.corrector = versor.corrector;
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}
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public void SetInverted(in DPVersor versor)
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{
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this.SetValues(
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(float)versor.GetScalar(),
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-(float)versor.GetX1(),
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-(float)versor.GetX2(),
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-(float)versor.GetX3()
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);
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}
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public readonly void Turn(in SPVector3 vector, out SPVector3 result)
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{
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float multiplier = 2.0f * this.corrector;
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float tx1 = multiplier * (this.x2 * vector.x3 - this.x3 * vector.x2);
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float tx2 = multiplier * (this.x3 * vector.x1 - this.x1 * vector.x3);
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float tx3 = multiplier * (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 SPVector3 vector, out SPVector3 result)
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{
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float multiplier = 2.0f * this.corrector;
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float tx1 = multiplier * (this.x2 * vector.x3 - this.x3 * vector.x2);
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float tx2 = multiplier * (this.x3 * vector.x1 - this.x1 * vector.x3);
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float tx3 = multiplier * (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 <= SPUtility.SQUARE_EPSYLON || (this.x1 * this.x1 + this.x2 * this.x2 + this.x3 * this.x3) <= SPUtility.SQUARE_EPSYLON * squareModule)
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{
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this.Reset();
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return;
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}
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float module = MathF.Sqrt(squareModule);
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this.s0 /= module;
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this.x1 /= module;
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this.x2 /= module;
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this.x3 /= module;
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this.corrector = (this.s0 * this.s0 + this.x1 * this.x1) + (this.x2 * this.x2 + this.x3 * this.x3);
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}
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public static void Combine(in SPVersor second, in SPVersor first, out SPVersor 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.corrector = 2.0f - squareModule;
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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 (squareModule < 1.0f - SPUtility.TWO_EPSYLON || 1.0f + SPUtility.TWO_EPSYLON < squareModule)
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{
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result.Normalize(squareModule);
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}
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}
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public static void LoadIdle(out SPVersor versor)
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{
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versor.corrector = 1.0f;
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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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}
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}
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