| | | 1 | | //======================================================================= |
| | | 2 | | // TriangleConeRimContacts.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 | | using System; |
| | | 9 | | using System.Runtime.CompilerServices; |
| | | 10 | | using static FixedMathSharp.Geometry.CylinderContactAlgebra; |
| | | 11 | | using static FixedMathSharp.Geometry.CircularRimContactAlgebra; |
| | | 12 | | |
| | | 13 | | namespace FixedMathSharp.Geometry; |
| | | 14 | | |
| | | 15 | | /// <summary>Admitted stationary triangle-edge/base-rim contacts of a finite cone.</summary> |
| | | 16 | | internal static class TriangleConeRimContacts |
| | | 17 | | { |
| | | 18 | | private const int ParameterSlots = 33; |
| | | 19 | | internal const int ValueCellWords = (16 * (ValueWords * 64 + 11) + 255) / 64; |
| | | 20 | | |
| | | 21 | | private struct Selection |
| | | 22 | | { |
| | | 23 | | internal bool HasValue, IsZero, IsRational; |
| | | 24 | | internal WideDirection3d First, Second; |
| | | 25 | | internal int Edge, ParameterOrdinal, ValueOrdinal, ValueShift; |
| | | 26 | | } |
| | | 27 | | |
| | | 28 | | internal static bool TryGetContact(in TriangleCircularGeometry geometry, FixedTriangle triangle, |
| | | 29 | | Fixed64 height, Fixed64 radius, scoped ConvexContactCandidate analytic, Fixed64 analyticDepth, |
| | | 30 | | out bool hasBetter, out Vector3d normal, out Vector3d radialPoint, |
| | | 31 | | out Vector3d trianglePoint, out Fixed64 depth, out bool clamped) |
| | | 32 | | { |
| | 80 | 33 | | int ValueWords = geometry.ValueWords; |
| | 80 | 34 | | int ValueCellWords = (16 * (geometry.ValueWords * 64 + 11) + 255) / 64; |
| | 160 | 35 | | hasBetter = false; normal = radialPoint = trianglePoint = default; |
| | 160 | 36 | | depth = analyticDepth; clamped = false; |
| | 80 | 37 | | Span<ulong> bestValues = stackalloc ulong[5 * ValueWords]; |
| | 80 | 38 | | Span<sbyte> bestSigns = stackalloc sbyte[5]; |
| | 80 | 39 | | Span<ulong> bestCell = stackalloc ulong[ValueCellWords]; |
| | 80 | 40 | | Selection best = default; |
| | 80 | 41 | | if (!TryKeepContacts(geometry, height, radius, analytic, analyticDepth, |
| | 80 | 42 | | bestValues, bestSigns, bestCell, ref best)) |
| | 1 | 43 | | return false; |
| | 79 | 44 | | if (!best.HasValue) |
| | 64 | 45 | | return true; |
| | 15 | 46 | | hasBetter = true; |
| | 15 | 47 | | GetContactMaterials(geometry, triangle, height, radius, bestValues, bestSigns, bestCell, best, |
| | 15 | 48 | | out normal, out radialPoint, out trianglePoint, out depth, out clamped); |
| | 15 | 49 | | return true; |
| | | 50 | | } |
| | | 51 | | |
| | | 52 | | private static bool TryKeepContacts(in TriangleCircularGeometry geometry, |
| | | 53 | | Fixed64 height, Fixed64 radius, scoped ConvexContactCandidate analytic, Fixed64 analyticDepth, |
| | | 54 | | scoped Span<ulong> bestValues, scoped Span<sbyte> bestSigns, scoped Span<ulong> bestCell, |
| | | 55 | | ref Selection best) |
| | | 56 | | { |
| | | 57 | | |
| | | 58 | | // The caller's exact face-width proof excludes a clamped analytic gap. |
| | | 59 | | // Its rounded value d bounds the original gap by d+1/2 raw, including Max. |
| | 80 | 60 | | ulong upperTwiceRaw = ((ulong)analyticDepth.m_rawValue << 1) | 1UL; |
| | 634 | 61 | | for (int edge = 0; edge < 3; edge++) |
| | | 62 | | { |
| | 238 | 63 | | WideDirection3d e = geometry.Edge(edge); |
| | | 64 | | // Horizontal edges are meridional; vertical edges are circular. |
| | | 65 | | // Their complete boundaries/principal radial directions are analytic. |
| | 238 | 66 | | if (e.Y.IsZero || e.X.IsZero && e.Z.IsZero) |
| | | 67 | | continue; |
| | 207 | 68 | | GetBasis(e, out WideDirection3d u, out WideDirection3d v); |
| | 1238 | 69 | | for (int firstSign = -1; firstSign <= 1; firstSign += 2) |
| | 2476 | 70 | | for (int secondSign = -1; secondSign <= 1; secondSign += 2) |
| | 4952 | 71 | | for (int chart = 0; chart < 2; chart++) |
| | | 72 | | { |
| | 1651 | 73 | | WideDirection3d first = firstSign > 0 ? u : -u; |
| | 1651 | 74 | | WideDirection3d second = secondSign > 0 ? v : -v; |
| | 2476 | 75 | | if (chart != 0) (first, second) = (second, first); |
| | 1651 | 76 | | if (!TryChart(geometry, height, radius, edge, first, second, |
| | 1651 | 77 | | analytic, upperTwiceRaw, bestValues, bestSigns, bestCell, ref best)) |
| | 1 | 78 | | return false; |
| | | 79 | | } |
| | | 80 | | } |
| | 79 | 81 | | return true; |
| | | 82 | | } |
| | | 83 | | |
| | | 84 | | private static void GetContactMaterials(in TriangleCircularGeometry geometry, FixedTriangle triangle, |
| | | 85 | | Fixed64 height, Fixed64 radius, ReadOnlySpan<ulong> bestValues, ReadOnlySpan<sbyte> bestSigns, |
| | | 86 | | Span<ulong> bestCell, in Selection best, out Vector3d normal, out Vector3d radialPoint, |
| | | 87 | | out Vector3d trianglePoint, out Fixed64 depth, out bool clamped) |
| | | 88 | | { |
| | | 89 | | |
| | 15 | 90 | | clamped = false; |
| | 15 | 91 | | GetMaterials(geometry, triangle, height, radius, best, out normal, out radialPoint, out trianglePoint); |
| | 15 | 92 | | if (best.IsZero) |
| | 1 | 93 | | depth = Fixed64.Zero; |
| | | 94 | | else |
| | | 95 | | { |
| | 14 | 96 | | FiniteAxisValueRoot root = Restore(bestValues, bestSigns, bestCell, best); |
| | 14 | 97 | | ConvexContactValueRoot.GetRoundedDepth(geometry.RawScale, geometry.ValueShift, |
| | 14 | 98 | | ref root, out depth, out clamped); |
| | | 99 | | } |
| | 14 | 100 | | } |
| | | 101 | | |
| | | 102 | | [MethodImpl(MethodImplOptions.NoInlining)] |
| | | 103 | | private static bool TryChart(in TriangleCircularGeometry geometry, Fixed64 height, Fixed64 radius, |
| | | 104 | | int edge, in WideDirection3d first, in WideDirection3d second, scoped ConvexContactCandidate analytic, ulong upp |
| | | 105 | | scoped Span<ulong> bestValues, scoped Span<sbyte> bestSigns, scoped Span<ulong> bestCell, |
| | | 106 | | ref Selection best) |
| | | 107 | | { |
| | 1651 | 108 | | int Words = geometry.ParameterWords; |
| | 1651 | 109 | | int ValueWords = geometry.ValueWords; |
| | 1651 | 110 | | int ValueCellWords = (16 * (geometry.ValueWords * 64 + 11) + 255) / 64; |
| | 1651 | 111 | | WideDirection3d outward = geometry.EdgeFromTo((edge + 2) % 3, edge); |
| | 3302 | 112 | | Signed832 a = WideDirection3d.Dot(first, outward), b = WideDirection3d.Dot(second, outward); |
| | | 113 | | // Each root needs positive outward projection a+t*b on t in (0,1]. |
| | | 114 | | // Nonpositive endpoints exclude the complete affine chart before construction. |
| | 1651 | 115 | | if (a.Sign <= 0 && WideArithmetic.AddSigned832(a, b).Sign <= 0) |
| | 649 | 116 | | return true; |
| | 1002 | 117 | | Span<ulong> data = stackalloc ulong[ParameterSlots * Words]; |
| | 1002 | 118 | | Span<sbyte> signs = stackalloc sbyte[ParameterSlots]; |
| | 1002 | 119 | | BuildConeParameter(geometry, height, radius, edge, first, second, data, signs); |
| | 1002 | 120 | | Span<ulong> batchCells = stackalloc ulong[64]; |
| | 1002 | 121 | | Span<int> batchShifts = stackalloc int[8]; |
| | 1002 | 122 | | FiniteAxisValueRoots roots = WideFiniteAxisIntersection.GetFiniteValueRoots( |
| | 1002 | 123 | | data[..(5 * Words)], signs[..5], batchCells, batchShifts); |
| | 1002 | 124 | | Span<ulong> cell = stackalloc ulong[WideFiniteAxisIntersection.GetFiniteValueRootCellWords( |
| | 1002 | 125 | | data[..(5 * Words)], signs[..5])]; |
| | 1002 | 126 | | Span<ulong> values = stackalloc ulong[5 * ValueWords]; |
| | 1002 | 127 | | Span<sbyte> valueSigns = stackalloc sbyte[5]; |
| | 1002 | 128 | | Span<ulong> valueCell = stackalloc ulong[ValueCellWords]; |
| | 3012 | 129 | | for (int ordinal = 0; ordinal < roots.Count; ordinal++) |
| | | 130 | | { |
| | 505 | 131 | | scoped FiniteAxisValueRoot root = FiniteAxisValueRoots.GetRoot(roots, ordinal, |
| | 505 | 132 | | data[..(5 * Words)], signs[..5], cell); |
| | 505 | 133 | | if (Sign(ref root, data, signs, 31, 2) <= 0) |
| | | 134 | | continue; |
| | | 135 | | // For negative n.Y, squaring is equivalent only with this sign |
| | | 136 | | // guard. Equality belongs to the earlier lateral-generator fan. |
| | 413 | 137 | | if (Sign(ref root, data, signs, 26, 2) < 0 |
| | 413 | 138 | | && Sign(ref root, data, signs, 28, 3) <= 0) |
| | | 139 | | continue; |
| | 318 | 140 | | int kSign = Sign(ref root, data, signs, 8, 2); |
| | 318 | 141 | | if (kSign == 0 || Sign(ref root, data, signs, 10, 3) != -kSign) |
| | | 142 | | continue; |
| | 167 | 143 | | int gapSign = Sign(ref root, data, signs, 13, 3) * kSign; |
| | 167 | 144 | | if (gapSign < 0) |
| | 1 | 145 | | return false; |
| | 166 | 146 | | if (best.IsZero || analytic.GapSign == 0) |
| | | 147 | | continue; |
| | 156 | 148 | | var candidate = new Selection |
| | 156 | 149 | | { |
| | 156 | 150 | | HasValue = true, First = first, Second = second, Edge = edge, |
| | 156 | 151 | | ParameterOrdinal = ordinal |
| | 156 | 152 | | }; |
| | 156 | 153 | | if (gapSign == 0) |
| | | 154 | | { |
| | 2 | 155 | | candidate.IsZero = true; best = candidate; |
| | 1 | 156 | | continue; |
| | | 157 | | } |
| | | 158 | | // Positive roots at or above the analytic half-raw upper bound |
| | | 159 | | // cannot win. Negative/zero gaps have already retained classification. |
| | 155 | 160 | | if (ConvexContactValueRoot.CompareSquaredGapToTwiceRaw(ref root, |
| | 155 | 161 | | data.Slice(16 * Words, 5 * Words), signs.Slice(16, 5), |
| | 155 | 162 | | data.Slice(21 * Words, 5 * Words), signs.Slice(21, 5), upperTwiceRaw) >= 0) |
| | | 163 | | continue; |
| | | 164 | | // Materialize only roots that survive feature admission and the |
| | | 165 | | // analytic bound. Rebuilding is valid for any number of survivors. |
| | 20 | 166 | | BuildValues(geometry.Edge(edge), geometry.CapOffset(edge, 1), geometry.Radius, geometry.ValueShift, values, |
| | 20 | 167 | | scoped FiniteAxisValueRoot value = ConvexContactValueRoot.MapSquaredValue( |
| | 20 | 168 | | geometry.RawScale, geometry.ValueShift, ref root, |
| | 20 | 169 | | data.Slice(16 * Words, 5 * Words), signs.Slice(16, 5), |
| | 20 | 170 | | data.Slice(21 * Words, 5 * Words), signs.Slice(21, 5), values, valueSigns, valueCell); |
| | 20 | 171 | | int comparison = best.HasValue |
| | 20 | 172 | | ? WideFiniteAxisIntersection.CompareFiniteValueRoots(value, Restore(bestValues, bestSigns, bestCell, bes |
| | 20 | 173 | | : ConvexContactValueRoot.CompareRootSquared(geometry.RawScale, geometry.ValueShift, ref value, analytic) |
| | 20 | 174 | | if (comparison >= 0) |
| | | 175 | | continue; |
| | 42 | 176 | | values.CopyTo(bestValues); valueSigns.CopyTo(bestSigns); valueCell.CopyTo(bestCell); |
| | 28 | 177 | | candidate.ValueOrdinal = value.Ordinal; candidate.ValueShift = value.DenominatorShift; |
| | 28 | 178 | | candidate.IsRational = value.IsRational; best = candidate; |
| | | 179 | | } |
| | 1001 | 180 | | return true; |
| | | 181 | | } |
| | | 182 | | |
| | | 183 | | [MethodImpl(MethodImplOptions.NoInlining)] |
| | | 184 | | private static void BuildConeParameter(in TriangleCircularGeometry geometry, Fixed64 height, Fixed64 radius, |
| | | 185 | | int edge, in WideDirection3d first, in WideDirection3d second, Span<ulong> data, Span<sbyte> signs) |
| | | 186 | | { |
| | | 187 | | |
| | 1017 | 188 | | BuildConeParameter(geometry.CapOffset(edge, 1), geometry.Radius, geometry.RawScale, |
| | 1017 | 189 | | height, radius, first, second, data, signs, useRigidBounds: !geometry.IsAffine); |
| | 1017 | 190 | | WideDirection3d outward = geometry.EdgeFromTo((edge + 2) % 3, edge); |
| | 1017 | 191 | | Write(data, signs, 31, WideDirection3d.Dot(outward, first)); |
| | 1017 | 192 | | Write(data, signs, 32, WideDirection3d.Dot(outward, second)); |
| | 1017 | 193 | | } |
| | | 194 | | |
| | | 195 | | // Writes the shared rim stationary chart and cone support switch into |
| | | 196 | | // slots 0..30. Triangle-only support walls occupy the following two slots. |
| | | 197 | | internal static void BuildConeParameter(in WideDirection3d offset, Signed576 scaledRadius, Signed320 rawScale, |
| | | 198 | | Fixed64 height, Fixed64 radius, in WideDirection3d first, in WideDirection3d second, |
| | | 199 | | Span<ulong> data, Span<sbyte> signs, bool useRigidBounds = false) |
| | | 200 | | { |
| | 1255 | 201 | | int Words = data.Length / signs.Length; |
| | 1255 | 202 | | BuildParameter(offset, scaledRadius, rawScale, first, second, data, signs, useRigidBounds); |
| | 1255 | 203 | | Write(data, signs, 26, Signed832.ExtendValue(first.Y)); |
| | 1255 | 204 | | Write(data, signs, 27, Signed832.ExtendValue(second.Y)); |
| | 2510 | 205 | | Signed192 h = Signed192.Raw(height), r = Signed192.Raw(radius); |
| | 2510 | 206 | | Signed320 hh = WideArithmetic.MultiplySigned192(h, h), rr = WideArithmetic.MultiplySigned192(r, r); |
| | 1255 | 207 | | Span<ulong> work = stackalloc ulong[3 * Words]; |
| | 10040 | 208 | | for (int index = 0; index < 3; index++) |
| | | 209 | | { |
| | 7530 | 210 | | WideDirection3d left = index < 2 ? first : second, right = index == 0 ? first : second; |
| | | 211 | | // Triangle axes <198 bits; segment affine-chart axes <200 bits. |
| | | 212 | | // Raw dimensions <63 give region coefficients <532 bits. The |
| | | 213 | | // forty-word magnitude owner retains both without narrowing. |
| | 7530 | 214 | | Signed832 radial = RadialDot(left, right), axial = WideArithmetic.MultiplySigned576(left.Y, right.Y); |
| | 7530 | 215 | | Import(radial, Slot(work, 0, Words)); Import(rr, Slot(work, 1, Words)); |
| | 3765 | 216 | | WideArithmetic.MultiplyMagnitudes(Slot(work, 0, Words), Slot(work, 1, Words), Slot(data, 28 + index, Words)) |
| | 3765 | 217 | | int sign = radial.Sign; |
| | 7530 | 218 | | Import(axial, Slot(work, 0, Words)); Import(hh, Slot(work, 1, Words)); |
| | 3765 | 219 | | WideArithmetic.MultiplyMagnitudes(Slot(work, 0, Words), Slot(work, 1, Words), Slot(work, 2, Words)); |
| | 3765 | 220 | | Add(Slot(work, 2, Words), -axial.Sign, Slot(data, 28 + index, Words), ref sign); |
| | 5020 | 221 | | if (index == 1) WideArithmetic.AddMagnitudeInto(Slot(data, 29, Words), Slot(data, 29, Words)); |
| | 3765 | 222 | | signs[28 + index] = (sbyte)sign; |
| | | 223 | | } |
| | 1255 | 224 | | } |
| | | 225 | | |
| | | 226 | | [MethodImpl(MethodImplOptions.NoInlining)] |
| | | 227 | | private static void GetMaterials(in TriangleCircularGeometry geometry, FixedTriangle triangle, |
| | | 228 | | Fixed64 height, Fixed64 radius, in Selection best, |
| | | 229 | | out Vector3d normal, out Vector3d radialPoint, out Vector3d trianglePoint) |
| | | 230 | | { |
| | 15 | 231 | | int Words = geometry.ParameterWords; |
| | 15 | 232 | | Span<ulong> data = stackalloc ulong[ParameterSlots * Words]; |
| | 15 | 233 | | Span<sbyte> signs = stackalloc sbyte[ParameterSlots]; |
| | 15 | 234 | | BuildConeParameter(geometry, height, radius, best.Edge, best.First, best.Second, data, signs); |
| | 15 | 235 | | Span<ulong> cell = stackalloc ulong[WideFiniteAxisIntersection.GetFiniteValueRootCellWords(data[..(5 * Words)], |
| | 15 | 236 | | bool found = WideFiniteAxisIntersection.TryGetFiniteValueRoot(data[..(5 * Words)], signs[..5], |
| | 15 | 237 | | best.ParameterOrdinal, cell, out FiniteAxisValueRoot root); |
| | | 238 | | System.Diagnostics.Debug.Assert(found); |
| | 15 | 239 | | trianglePoint = TriangleCylinderRimWitnesses.GetRootPoint(geometry, triangle, best.Edge, best.First, best.Second |
| | 15 | 240 | | Span<ulong> gradient = stackalloc ulong[54]; |
| | 15 | 241 | | Span<sbyte> gradientSigns = stackalloc sbyte[6]; |
| | 15 | 242 | | WriteGradient(best.First, best.Second, gradient, gradientSigns); |
| | 30 | 243 | | gradient.Slice(18, 18).Clear(); gradientSigns.Slice(2, 2).Clear(); |
| | 15 | 244 | | radialPoint = ConvexContactValueRoot.GetScaledNormalizedDirection(ref root, gradient, gradientSigns, radius, -1) |
| | 15 | 245 | | WriteGradient(Transform(geometry.WorldBasis, best.First), Transform(geometry.WorldBasis, best.Second), gradient, |
| | 15 | 246 | | normal = ConvexContactValueRoot.GetNormalizedDirection(ref root, gradient, gradientSigns, 1); |
| | 15 | 247 | | } |
| | | 248 | | |
| | | 249 | | private static FiniteAxisValueRoot Restore(ReadOnlySpan<ulong> values, ReadOnlySpan<sbyte> signs, |
| | 20 | 250 | | Span<ulong> cell, in Selection selection) => new() |
| | 20 | 251 | | { |
| | 20 | 252 | | Coefficients = values, Signs = signs, LowerNumerator = cell, |
| | 20 | 253 | | DenominatorShift = selection.ValueShift, Ordinal = selection.ValueOrdinal, IsRational = selection.IsRational |
| | 20 | 254 | | }; |
| | | 255 | | } |