| | | 1 | | //======================================================================= |
| | | 2 | | // WideRigidProjection.cs |
| | | 3 | | //======================================================================= |
| | | 4 | | // MIT License, Copyright (c) 2024-present David Oravsky (mrdav30) |
| | | 5 | | // See LICENSE file in the project root for full license information. |
| | | 6 | | //======================================================================= |
| | | 7 | | |
| | | 8 | | namespace FixedMathSharp.Geometry; |
| | | 9 | | |
| | | 10 | | /// <summary> |
| | | 11 | | /// Owns exact rigid-axis transforms and projection arithmetic shared by wide |
| | | 12 | | /// geometry relations. |
| | | 13 | | /// </summary> |
| | | 14 | | internal static class WideRigidProjection |
| | | 15 | | { |
| | | 16 | | internal static WideAxis3 TransformLocalAxis( |
| | | 17 | | in WideRationalBasis3d basis, |
| | | 18 | | Signed192 localX, |
| | | 19 | | Signed192 localY, |
| | | 20 | | Signed192 localZ) => |
| | 377925 | 21 | | new( |
| | 377925 | 22 | | TransformLocalAxisComponent( |
| | 377925 | 23 | | localX, localY, localZ, |
| | 377925 | 24 | | basis.Xx, basis.Yx, basis.Zx), |
| | 377925 | 25 | | TransformLocalAxisComponent( |
| | 377925 | 26 | | localX, localY, localZ, |
| | 377925 | 27 | | basis.Xy, basis.Yy, basis.Zy), |
| | 377925 | 28 | | TransformLocalAxisComponent( |
| | 377925 | 29 | | localX, localY, localZ, |
| | 377925 | 30 | | basis.Xz, basis.Yz, basis.Zz)); |
| | | 31 | | |
| | | 32 | | /// <summary> |
| | | 33 | | /// Transforms a local triangle normal-cross-edge axis. The local components |
| | | 34 | | /// must come from that exact construction; its proven rigid-triangle bound |
| | | 35 | | /// keeps each transformed component within <see cref="Signed320"/>. |
| | | 36 | | /// </summary> |
| | | 37 | | internal static WideAxis3 TransformLocalTriangleNormalCrossEdgeAxis( |
| | | 38 | | in WideRationalBasis3d basis, |
| | | 39 | | Signed320 localX, |
| | | 40 | | Signed320 localY, |
| | | 41 | | Signed320 localZ) => |
| | 585 | 42 | | new( |
| | 585 | 43 | | TransformLocalTriangleNormalCrossEdgeComponent( |
| | 585 | 44 | | localX, localY, localZ, |
| | 585 | 45 | | basis.Xx, basis.Yx, basis.Zx), |
| | 585 | 46 | | TransformLocalTriangleNormalCrossEdgeComponent( |
| | 585 | 47 | | localX, localY, localZ, |
| | 585 | 48 | | basis.Xy, basis.Yy, basis.Zy), |
| | 585 | 49 | | TransformLocalTriangleNormalCrossEdgeComponent( |
| | 585 | 50 | | localX, localY, localZ, |
| | 585 | 51 | | basis.Xz, basis.Yz, basis.Zz)); |
| | | 52 | | |
| | | 53 | | /// <summary>Transforms a raw finite face normal crossed with a raw finite edge, preserving its exact local construc |
| | | 54 | | internal static WideAxis3 TransformLocalNormalCrossEdge( |
| | | 55 | | in WideRationalBasis3d basis, |
| | | 56 | | Signed192 normalX, Signed192 normalY, Signed192 normalZ, |
| | | 57 | | Signed192 edgeX, Signed192 edgeY, Signed192 edgeZ) => |
| | 585 | 58 | | TransformLocalTriangleNormalCrossEdgeAxis(basis, |
| | 585 | 59 | | WideArithmetic.MultiplySubtract(normalY, edgeZ, normalZ, edgeY), |
| | 585 | 60 | | WideArithmetic.MultiplySubtract(normalZ, edgeX, normalX, edgeZ), |
| | 585 | 61 | | WideArithmetic.MultiplySubtract(normalX, edgeY, normalY, edgeX)); |
| | | 62 | | |
| | | 63 | | internal static void GetLocalAxisProjections( |
| | | 64 | | in WideAxis3 axis, |
| | | 65 | | in WideRationalBasis3d basis, |
| | | 66 | | out Signed576 x, |
| | | 67 | | out Signed576 y, |
| | | 68 | | out Signed576 z) |
| | | 69 | | { |
| | 44017 | 70 | | x = GetBasisAxisProjection( |
| | 44017 | 71 | | axis, |
| | 44017 | 72 | | basis.Xx, |
| | 44017 | 73 | | basis.Xy, |
| | 44017 | 74 | | basis.Xz); |
| | 44017 | 75 | | y = GetBasisAxisProjection( |
| | 44017 | 76 | | axis, |
| | 44017 | 77 | | basis.Yx, |
| | 44017 | 78 | | basis.Yy, |
| | 44017 | 79 | | basis.Yz); |
| | 44017 | 80 | | z = GetBasisAxisProjection( |
| | 44017 | 81 | | axis, |
| | 44017 | 82 | | basis.Zx, |
| | 44017 | 83 | | basis.Zy, |
| | 44017 | 84 | | basis.Zz); |
| | 44017 | 85 | | } |
| | | 86 | | |
| | | 87 | | internal static Signed576 GetLocalOffsetProjection( |
| | | 88 | | Vector3d localOffset, |
| | | 89 | | in Signed576 axisX, |
| | | 90 | | in Signed576 axisY, |
| | | 91 | | in Signed576 axisZ) => |
| | 135515 | 92 | | WideArithmetic.AddSigned576( |
| | 135515 | 93 | | WideArithmetic.AddSigned576( |
| | 135515 | 94 | | WideArithmetic.MultiplySigned576( |
| | 135515 | 95 | | axisX, |
| | 135515 | 96 | | localOffset.X.m_rawValue), |
| | 135515 | 97 | | WideArithmetic.MultiplySigned576( |
| | 135515 | 98 | | axisY, |
| | 135515 | 99 | | localOffset.Y.m_rawValue)), |
| | 135515 | 100 | | WideArithmetic.MultiplySigned576( |
| | 135515 | 101 | | axisZ, |
| | 135515 | 102 | | localOffset.Z.m_rawValue)); |
| | | 103 | | |
| | | 104 | | internal static void TransformLocalAxis( |
| | | 105 | | in WideRationalBasis3d basis, |
| | | 106 | | in WideAxis3 localAxis, |
| | | 107 | | out Signed576 x, |
| | | 108 | | out Signed576 y, |
| | | 109 | | out Signed576 z) |
| | | 110 | | { |
| | 23160 | 111 | | x = TransformLocalAxisComponent( |
| | 23160 | 112 | | localAxis, |
| | 23160 | 113 | | basis.Xx, |
| | 23160 | 114 | | basis.Yx, |
| | 23160 | 115 | | basis.Zx); |
| | 23160 | 116 | | y = TransformLocalAxisComponent( |
| | 23160 | 117 | | localAxis, |
| | 23160 | 118 | | basis.Xy, |
| | 23160 | 119 | | basis.Yy, |
| | 23160 | 120 | | basis.Zy); |
| | 23160 | 121 | | z = TransformLocalAxisComponent( |
| | 23160 | 122 | | localAxis, |
| | 23160 | 123 | | basis.Xz, |
| | 23160 | 124 | | basis.Yz, |
| | 23160 | 125 | | basis.Zz); |
| | 23160 | 126 | | } |
| | | 127 | | |
| | | 128 | | internal static Signed576 GetWorldOriginDifferenceProjection( |
| | | 129 | | Vector3d end, |
| | | 130 | | Vector3d start, |
| | | 131 | | in WideAxis3 axis) => |
| | 9475 | 132 | | WideArithmetic.AddSigned576( |
| | 9475 | 133 | | WideArithmetic.AddSigned576( |
| | 9475 | 134 | | WideArithmetic.MultiplySigned320( |
| | 9475 | 135 | | Signed320.ExtendValue(WideArithmetic.SubtractSigned192( |
| | 9475 | 136 | | Signed192.Raw(end.X), |
| | 9475 | 137 | | Signed192.Raw(start.X))), |
| | 9475 | 138 | | axis.X), |
| | 9475 | 139 | | WideArithmetic.MultiplySigned320( |
| | 9475 | 140 | | Signed320.ExtendValue(WideArithmetic.SubtractSigned192( |
| | 9475 | 141 | | Signed192.Raw(end.Y), |
| | 9475 | 142 | | Signed192.Raw(start.Y))), |
| | 9475 | 143 | | axis.Y)), |
| | 9475 | 144 | | WideArithmetic.MultiplySigned320( |
| | 9475 | 145 | | Signed320.ExtendValue(WideArithmetic.SubtractSigned192( |
| | 9475 | 146 | | Signed192.Raw(end.Z), |
| | 9475 | 147 | | Signed192.Raw(start.Z))), |
| | 9475 | 148 | | axis.Z)); |
| | | 149 | | |
| | | 150 | | internal static Signed576 GetBasisAxisProjection( |
| | | 151 | | in WideAxis3 axis, |
| | | 152 | | Signed192 basisX, |
| | | 153 | | Signed192 basisY, |
| | | 154 | | Signed192 basisZ) => |
| | 136308 | 155 | | WideArithmetic.AddSigned576( |
| | 136308 | 156 | | WideArithmetic.AddSigned576( |
| | 136308 | 157 | | WideArithmetic.MultiplySigned576( |
| | 136308 | 158 | | Signed576.ExtendValue(axis.X), |
| | 136308 | 159 | | basisX), |
| | 136308 | 160 | | WideArithmetic.MultiplySigned576( |
| | 136308 | 161 | | Signed576.ExtendValue(axis.Y), |
| | 136308 | 162 | | basisY)), |
| | 136308 | 163 | | WideArithmetic.MultiplySigned576( |
| | 136308 | 164 | | Signed576.ExtendValue(axis.Z), |
| | 136308 | 165 | | basisZ)); |
| | | 166 | | |
| | | 167 | | internal static void IncludeProjection( |
| | | 168 | | in Signed576 candidate, |
| | | 169 | | ref Signed576 minimum, |
| | | 170 | | ref Signed576 maximum) |
| | | 171 | | { |
| | 105062 | 172 | | if (WideArithmetic.SubtractSigned576(candidate, minimum).Sign < 0) |
| | 12488 | 173 | | minimum = candidate; |
| | 105062 | 174 | | if (WideArithmetic.SubtractSigned576(candidate, maximum).Sign > 0) |
| | 13337 | 175 | | maximum = candidate; |
| | 105062 | 176 | | } |
| | | 177 | | |
| | | 178 | | private static Signed320 TransformLocalAxisComponent( |
| | | 179 | | Signed192 localX, |
| | | 180 | | Signed192 localY, |
| | | 181 | | Signed192 localZ, |
| | | 182 | | Signed192 basisX, |
| | | 183 | | Signed192 basisY, |
| | | 184 | | Signed192 basisZ) => |
| | 1133775 | 185 | | WideArithmetic.AddSigned320( |
| | 1133775 | 186 | | WideArithmetic.AddSigned320( |
| | 1133775 | 187 | | WideArithmetic.MultiplySigned192(localX, basisX), |
| | 1133775 | 188 | | WideArithmetic.MultiplySigned192(localY, basisY)), |
| | 1133775 | 189 | | WideArithmetic.MultiplySigned192(localZ, basisZ)); |
| | | 190 | | |
| | | 191 | | private static Signed320 TransformLocalTriangleNormalCrossEdgeComponent( |
| | | 192 | | Signed320 localX, |
| | | 193 | | Signed320 localY, |
| | | 194 | | Signed320 localZ, |
| | | 195 | | Signed192 basisX, |
| | | 196 | | Signed192 basisY, |
| | | 197 | | Signed192 basisZ) |
| | | 198 | | { |
| | 1755 | 199 | | Signed576 transformed = WideArithmetic.AddSigned576( |
| | 1755 | 200 | | WideArithmetic.AddSigned576( |
| | 1755 | 201 | | WideArithmetic.MultiplySigned576( |
| | 1755 | 202 | | Signed576.ExtendValue(localX), |
| | 1755 | 203 | | basisX), |
| | 1755 | 204 | | WideArithmetic.MultiplySigned576( |
| | 1755 | 205 | | Signed576.ExtendValue(localY), |
| | 1755 | 206 | | basisY)), |
| | 1755 | 207 | | WideArithmetic.MultiplySigned576( |
| | 1755 | 208 | | Signed576.ExtendValue(localZ), |
| | 1755 | 209 | | basisZ)); |
| | 1755 | 210 | | return Signed320.NarrowValue(transformed); |
| | | 211 | | } |
| | | 212 | | |
| | | 213 | | private static Signed576 TransformLocalAxisComponent( |
| | | 214 | | in WideAxis3 localAxis, |
| | | 215 | | Signed192 basisX, |
| | | 216 | | Signed192 basisY, |
| | | 217 | | Signed192 basisZ) => |
| | 69480 | 218 | | WideArithmetic.AddSigned576( |
| | 69480 | 219 | | WideArithmetic.AddSigned576( |
| | 69480 | 220 | | WideArithmetic.MultiplySigned576( |
| | 69480 | 221 | | Signed576.ExtendValue(localAxis.X), |
| | 69480 | 222 | | basisX), |
| | 69480 | 223 | | WideArithmetic.MultiplySigned576( |
| | 69480 | 224 | | Signed576.ExtendValue(localAxis.Y), |
| | 69480 | 225 | | basisY)), |
| | 69480 | 226 | | WideArithmetic.MultiplySigned576( |
| | 69480 | 227 | | Signed576.ExtendValue(localAxis.Z), |
| | 69480 | 228 | | basisZ)); |
| | | 229 | | } |