LowLevelMesh shape shifting with Marching Cubes and SDF interpolation

edgeTable.h

#ifndef edgeTable_h
#define edgeTable_h

constant int edgeTable[256]={
0x0  , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0   };

#endif /* edgeTable_h */

SDFPrimitives.metal

#include <metal_stdlib>
using namespace metal;

#define SDFShapeTypeSphere      0u
#define SDFShapeTypeBox         1u
#define SDFShapeTypeTorus       2u
#define SDFShapeTypeRoundedBox  3u
#define SDFShapeTypeBoxFrame    4u
#define SDFShapeTypeLink        5u
#define SDFShapeTypeOctahedron  6u

inline float sdf_sphere(float3 p, float3 c, float r) {
    return length(p - c) - r;
}

inline float sdf_box(float3 p, float3 c, float3 b) {
    float3 d = abs(p - c) - b;
    return length(max(d, float3(0.0))) + min(max(d.x, max(d.y, d.z)), 0.0);
}

inline float sdf_torus(float3 p, float3 c, float R, float r) {
    float3 q = p - c;
    float2 k = float2(length(q.xz) - R, q.y);
    return length(k) - r;
}

inline float sdf_rounded_box(float3 p, float3 c, float3 b, float cr) {
    float3 q = abs(p - c) - (b - cr);
    return length(max(q, 0.0)) + min(max(q.x, max(q.y, q.z)), 0.0) - cr;
}

inline float sdf_box_frame(float3 p, float3 c, float3 b, float e) {
    float3 pp = abs(p - c) - b;
    float3 q  = abs(pp + e) - e;

    float3 v1 = float3(pp.x, q.y,  q.z);
    float3 v2 = float3(q.x,  pp.y, q.z);
    float3 v3 = float3(q.x,  q.y,  pp.z);

    float d1 = length(max(v1, 0.0)) + min(max(pp.x, max(q.y, q.z)), 0.0);
    float d2 = length(max(v2, 0.0)) + min(max(q.x,  max(pp.y, q.z)), 0.0);
    float d3 = length(max(v3, 0.0)) + min(max(q.x,  max(q.y,  pp.z)), 0.0);

    return min(min(d1, d2), d3);
}

inline float sdf_link(float3 p, float3 c, float le, float r1, float r2) {
    float3 q = float3(p.x - c.x, max(abs(p.y - c.y) - le, 0.0), p.z - c.z);
    return length(float2(length(q.xy) - r1, q.z)) - r2;
}

inline float sdf_octahedron(float3 p, float3 c, float s) {
    float3 pp = abs(p - c);
    return (pp.x + pp.y + pp.z - s) * 0.57735027; // 1/sqrt(3)
}

// Single-radius presets sized from a common bounding radius
inline float sdf_for_shape(uint shapeType, float3 p, float3 center, float radius) {
    switch (shapeType) {
        default:
        case SDFShapeTypeSphere:
            return sdf_sphere(p, center, radius);
        case SDFShapeTypeBox: {
            float s = radius / sqrt(3.0f);
            return sdf_box(p, center, float3(s));
        }
        case SDFShapeTypeTorus: {
            float R = radius * 0.65f;
            float r = radius * 0.28f;
            return sdf_torus(p, center, R, r);
        }
        case SDFShapeTypeRoundedBox: {
            float s  = radius / sqrt(3.0f);
            float cr = s * 0.3f;
            return sdf_rounded_box(p, center, float3(s), cr);
        }
        case SDFShapeTypeBoxFrame: {
            float s = radius / sqrt(3.0f);
            float e = s * 0.20f;
            return sdf_box_frame(p, center, float3(s), e);
        }
        case SDFShapeTypeLink: {
            float le = radius * 0.25f;
            float r1 = radius * 0.6f;
            float r2 = radius * 0.15f;
            return sdf_link(p, center, le, r1, r2);
        }
        case SDFShapeTypeOctahedron: {
            float s = radius * 1.0f;
            return sdf_octahedron(p, center, s);
        }
    }
}

// Domain repetition
inline float3 opRepetition(float3 p, uint count, float radius) {
    if (count <= 1) return p;
    
    // Reduce the effective radius
    float effectiveRadius = radius * 0.6;
    
    // Calculate spacing
    float spacing = 2.0 * effectiveRadius / float(count);
    
    // Limit the repetition
    float3 q = p;
    q.x = p.x - spacing * clamp(round(p.x / spacing), -float(count-1)/2.0, float(count-1)/2.0);
    q.y = p.y - spacing * clamp(round(p.y / spacing), -float(count-1)/2.0, float(count-1)/2.0);
    q.z = p.z - spacing * clamp(round(p.z / spacing), -float(count-1)/2.0, float(count-1)/2.0);
    
    return q;
}

// Apply repetition to SDF shapes with radius scaling
inline float sdf_with_repetition(uint shapeType, float3 p, float3 center, float radius, 
                                uint repetition) {
    if (repetition <= 1) {
        // No repetition, use original SDF
        return sdf_for_shape(shapeType, p, center, radius);
    }
    
    // Scale radius down more aggressively to prevent overlap
    float scaledRadius = radius / (float(repetition) * 2.0);
    
    // Apply repetition transformation using radius for spacing
    float3 q = opRepetition(p, repetition, radius);
    
    return sdf_for_shape(shapeType, q, center, scaledRadius);
}

SDFShape.swift

import Foundation

enum SDFShape: UInt32, CaseIterable {
    case sphere     = 0
    case box        = 1
    case torus      = 2
    case roundedBox = 3
    case boxFrame   = 4
    case link       = 5
    case octahedron = 6
}

shapeShiftingSDFMarchingCubesMesh.metal

#include <metal_stdlib>
using namespace metal;

#include "VertexPositionNormal.h"
#include "ShapeShiftingSDFMarchingCubesParams.h"
#include "edgeTable.h"
#include "triTable.h"
#include "SDFPrimitives.metal"

inline float3 interpolateIsoSurfacePosition(float3 pA, float valueA,
                                            float3 pB, float valueB,
                                            float isoLevel) {
    float denom = (valueB - valueA);
    float t = (isoLevel - valueA) / (denom + 1e-6f);
    return mix(pA, pB, clamp(t, 0.0f, 1.0f));
}

// Blend between two SDF primitives chosen by ids (shape0, shape1)
inline float fieldValue(float3 worldPos, constant ShapeShiftingSDFMarchingCubesParams& P) {
    float d0 = sdf_with_repetition(P.shape0, worldPos, P.center, P.radius, P.repetition0);
    float d1 = sdf_with_repetition(P.shape1, worldPos, P.center, P.radius, P.repetition1);
    return mix(d0, d1, clamp(P.blendT, 0.0f, 1.0f));
}

inline float3 estimateNormalFromField(float3 worldPos, constant ShapeShiftingSDFMarchingCubesParams& P) {
    float h = 0.5f * min(P.cellSize.x, min(P.cellSize.y, P.cellSize.z));
    float fx = fieldValue(worldPos + float3(h,0,0), P) - fieldValue(worldPos - float3(h,0,0), P);
    float fy = fieldValue(worldPos + float3(0,h,0), P) - fieldValue(worldPos - float3(0,h,0), P);
    float fz = fieldValue(worldPos + float3(0,0,h), P) - fieldValue(worldPos - float3(0,0,h), P);
    return normalize(float3(fx, fy, fz) / (2.0f * h));
}

kernel void shapeShiftingSDFMarchingCubesMesh(device VertexPositionNormal*  outVertices      [[buffer(0)]],
                                              device uint*                  outIndices       [[buffer(1)]],
                                              device atomic_uint*           outVertexCounter [[buffer(2)]],
                                              constant ShapeShiftingSDFMarchingCubesParams& P       [[buffer(3)]],
                                              uint3 cellCoord [[thread_position_in_grid]]) {
    if (cellCoord.x >= P.cells.x || cellCoord.y >= P.cells.y || cellCoord.z >= P.cells.z) return;

    const int3 cornerOffsets[8] = {
        int3(0,0,0), int3(1,0,0), int3(1,1,0), int3(0,1,0),
        int3(0,0,1), int3(1,0,1), int3(1,1,1), int3(0,1,1)
    };

    const int2 edgeCornerIndexPairs[12] = {
        int2(0,1), int2(1,2), int2(2,3), int2(3,0),
        int2(4,5), int2(5,6), int2(6,7), int2(7,4),
        int2(0,4), int2(1,5), int2(2,6), int2(3,7)
    };

    const float3 cellOriginWS = P.origin + float3(cellCoord) * P.cellSize;

    float   cornerScalar[8];
    float3  cornerPositionWS[8];
    for (int i = 0; i < 8; ++i) {
        float3 cp = cellOriginWS + float3(cornerOffsets[i]) * P.cellSize;
        cornerPositionWS[i] = cp;
        cornerScalar[i]     = fieldValue(cp, P);
    }

    int cubeIndex = 0;
    if (cornerScalar[0] > P.isoLevel) cubeIndex |=   1;
    if (cornerScalar[1] > P.isoLevel) cubeIndex |=   2;
    if (cornerScalar[2] > P.isoLevel) cubeIndex |=   4;
    if (cornerScalar[3] > P.isoLevel) cubeIndex |=   8;
    if (cornerScalar[4] > P.isoLevel) cubeIndex |=  16;
    if (cornerScalar[5] > P.isoLevel) cubeIndex |=  32;
    if (cornerScalar[6] > P.isoLevel) cubeIndex |=  64;
    if (cornerScalar[7] > P.isoLevel) cubeIndex |= 128;

    int edgeMask = edgeTable[cubeIndex];
    if (edgeMask == 0) return;

    float3 edgeIntersectionWS[12];
    for (int edge = 0; edge < 12; ++edge) {
        if (edgeMask & (1 << edge)) {
            const int a = edgeCornerIndexPairs[edge].x;
            const int b = edgeCornerIndexPairs[edge].y;
            edgeIntersectionWS[edge] = interpolateIsoSurfacePosition(
                cornerPositionWS[a], cornerScalar[a],
                cornerPositionWS[b], cornerScalar[b],
                P.isoLevel
            );
        }
    }

    constant int* triangleEdgesRow = &triTable[cubeIndex][0];

    for (int triIdx = 0; triIdx < 16 && triangleEdgesRow[triIdx] != -1; triIdx += 3) {
        const int e0 = triangleEdgesRow[triIdx + 0];
        const int e1 = triangleEdgesRow[triIdx + 1];
        const int e2 = triangleEdgesRow[triIdx + 2];

        const float3 p0 = edgeIntersectionWS[e0];
        const float3 p1 = edgeIntersectionWS[e1];
        const float3 p2 = edgeIntersectionWS[e2];

        const float3 n0 = estimateNormalFromField(p0, P);
        const float3 n1 = estimateNormalFromField(p1, P);
        const float3 n2 = estimateNormalFromField(p2, P);

        const uint baseVertexIndex = atomic_fetch_add_explicit(outVertexCounter, (uint)3, memory_order_relaxed);

        outVertices[baseVertexIndex + 0].position = p0;
        outVertices[baseVertexIndex + 0].normal   = n0;
        outVertices[baseVertexIndex + 1].position = p1;
        outVertices[baseVertexIndex + 1].normal   = n1;
        outVertices[baseVertexIndex + 2].position = p2;
        outVertices[baseVertexIndex + 2].normal   = n2;

        outIndices[baseVertexIndex + 0] = baseVertexIndex + 0;
        outIndices[baseVertexIndex + 1] = baseVertexIndex + 1;
        outIndices[baseVertexIndex + 2] = baseVertexIndex + 2;
    }
}

ShapeShiftingSDFMarchingCubesParams.h

#ifndef SingleSDFMarchingCubesParams_h
#define SingleSDFMarchingCubesParams_h

#include <simd/simd.h>

struct ShapeShiftingSDFMarchingCubesParams {
    simd_uint3  cells;
    simd_float3 origin;
    simd_float3 cellSize;
    float       isoLevel;
    simd_float3 center;
    float       radius;
    float       blendT;
    uint32_t    shape0;
    uint32_t    shape1;
    uint32_t    repetition0;
    uint32_t    repetition1;
};

#endif /* SingleSDFMarchingCubesParams_h */

ShapeShiftingSDFMarchingCubesView.swift

import SwiftUI
import RealityKit
import Metal

struct ShapeShiftingSDFMarchingCubesView: View {
    @State private var entity: Entity?
    @State private var mesh: LowLevelMesh?
    @State private var timer: Timer?
    @State private var interpolationAmount: Float = 0
    @State private var directionForward: Bool = true
    @State private var animationRate: Float = 1.5
    @State private var dwellTime: Float = 0
    @State private var maxDwellTime: Float = 1.0
    @State private var shape0: SDFShape = .sphere
    @State private var repetition0: UInt32 = 1
    @State private var shape1: SDFShape = .box
    @State private var repetition1: UInt32 = 1
    @State private var lastSwapEnd: Int = 0
    @State private var rotationAngles: SIMD3<Float> = [0, 0, 0]
    @State private var lastRotationUpdateTime = CACurrentMediaTime()

    let device: MTLDevice
    let commandQueue: MTLCommandQueue
    let computePipelineState: MTLComputePipelineState
    let vertexCountBuffer: MTLBuffer

    let radius: Float = 0.175
    var cellsPerAxis: UInt32 = 80
    var cells: SIMD3<UInt32> {
        return SIMD3<UInt32>(cellsPerAxis, cellsPerAxis, cellsPerAxis)
    }
    var cellSize: SIMD3<Float> {
        let ratio = radius / Float(cellsPerAxis) * 2
        return SIMD3<Float>(ratio, ratio, ratio)
    }

    var material: PhysicallyBasedMaterial {
        var m = PhysicallyBasedMaterial()
        m.roughness = .init(floatLiteral: 0.0)
        m.metallic = .init(floatLiteral: 1.0)
        return m
    }

    init() {
        let device = MTLCreateSystemDefaultDevice()!
        self.device = device
        self.commandQueue = device.makeCommandQueue()!
        let library = device.makeDefaultLibrary()!
        let function = library.makeFunction(name: "shapeShiftingSDFMarchingCubesMesh")!
        self.computePipelineState = try! device.makeComputePipelineState(function: function)
        self.vertexCountBuffer = device.makeBuffer(length: MemoryLayout<UInt32>.stride, options: .storageModeShared)!
    }

    var body: some View {
        VStack(spacing: 160) {
            RealityView { content in
                let maxCellCount = Int(cells.x * cells.y * cells.z)
                let vertexCapacity = 15 * maxCellCount
                let indexCapacity = vertexCapacity

                let lowLevelMesh = try! VertexPositionNormal.initializeMesh(vertexCapacity: vertexCapacity,
                                                                            indexCapacity: indexCapacity)
                let meshResource = try! await MeshResource(from: lowLevelMesh)
                let entity = ModelEntity(mesh: meshResource, materials: [material])
                content.add(entity)
                self.mesh = lowLevelMesh
                self.entity = entity
                startTimer()
            }
            .onDisappear { stopTimer() }

            VStack {
                HStack {
                    Text("Animation Rate: \(animationRate, specifier: "%.2fx")")
                    Spacer()
                    Slider(value: $animationRate, in: 0.5...2)
                        .frame(width: 300)
                }
                
                HStack {
                    Text("Dwell Time: \(maxDwellTime, specifier: "%.2f")s")
                    Spacer()
                    Slider(value: $maxDwellTime, in: 0.0...2.0)
                        .frame(width: 300)
                }
            }
            .frame(width: 500)
            .padding()
            .glassBackgroundEffect()
        }
    }

    func startTimer() {
        stopTimer()
        timer = Timer.scheduledTimer(withTimeInterval: 1.0 / 60.0, repeats: true) { _ in
            
            let currentTime = CACurrentMediaTime()
            let frameDuration = currentTime - lastRotationUpdateTime

            let deltaInterpolation = Float(frameDuration) * animationRate
            interpolationAmount += directionForward ? deltaInterpolation : -deltaInterpolation

            // Handle dwell time at the ends
            if interpolationAmount >= 1.0 {
                if dwellTime < maxDwellTime {
                    dwellTime += Float(frameDuration)
                    interpolationAmount = 1.0
                } else {
                    // Dwell time complete, start transitioning
                    if lastSwapEnd != 1 {
                        shape0 = randomShape(excluding: shape1)
                        repetition0 = randomizeRepetition()
                        lastSwapEnd = 1
                    }
                    interpolationAmount = 1.0
                    directionForward = false
                    dwellTime = 0 // Reset dwell counter
                }
            } else if interpolationAmount <= 0 {
                if dwellTime < maxDwellTime {
                    dwellTime += Float(frameDuration)
                    interpolationAmount = 0
                } else {
                    // Dwell time complete, start transitioning
                    if lastSwapEnd != 0 {
                        shape1 = randomShape(excluding: shape0)
                        repetition1 = randomizeRepetition()
                        lastSwapEnd = 0
                    }
                    interpolationAmount = 0
                    directionForward = true
                    dwellTime = 0 // Reset dwell counter
                }
            }

            updateMesh()
            
            // Rotate along all axis at different rates for a wonky roll effect
            let rotationMultiplier: Float = 1.25
            rotationAngles.x += Float(frameDuration * 0.25) * rotationMultiplier
            rotationAngles.y += Float(frameDuration * 0.125) * rotationMultiplier
            rotationAngles.z += Float(frameDuration * 0.0675) * rotationMultiplier
            
            let rotationX = simd_quatf(angle: rotationAngles.x, axis: [1, 0, 0])
            let rotationY = simd_quatf(angle: rotationAngles.y, axis: [0, 1, 0])
            let rotationZ = simd_quatf(angle: rotationAngles.z, axis: [0, 0, 1])
            entity?.transform.rotation = rotationX * rotationY * rotationZ
            
            lastRotationUpdateTime = currentTime
        }
    }

    func stopTimer() {
        timer?.invalidate()
        timer = nil
    }

    func updateMesh() {
        guard let mesh = mesh,
              let commandBuffer = commandQueue.makeCommandBuffer(),
              let computeEncoder = commandBuffer.makeComputeCommandEncoder()
        else { return }

        let gridSizeWorldSpace = SIMD3<Float>(Float(cells.x), Float(cells.y), Float(cells.z)) * cellSize
        let gridMinCornerWorldSpace = -0.5 * gridSizeWorldSpace
        let gridMaxCornerWorldSpace = gridMinCornerWorldSpace + gridSizeWorldSpace

        var params = ShapeShiftingSDFMarchingCubesParams(
            cells: cells,
            origin: gridMinCornerWorldSpace,
            cellSize: cellSize,
            isoLevel: 0.0,
            center: SIMD3<Float>(0, 0, 0),
            radius: radius,
            blendT: interpolationAmount,
            shape0: shape0.rawValue,
            shape1: shape1.rawValue,
            repetition0: repetition0,
            repetition1: repetition1
        )

        vertexCountBuffer.contents().bindMemory(to: UInt32.self, capacity: 1).pointee = 0

        let vertexBuffer = mesh.replace(bufferIndex: 0, using: commandBuffer)
        let indexBuffer = mesh.replaceIndices(using: commandBuffer)

        computeEncoder.setComputePipelineState(computePipelineState)
        computeEncoder.setBuffer(vertexBuffer, offset: 0, index: 0)
        computeEncoder.setBuffer(indexBuffer, offset: 0, index: 1)
        computeEncoder.setBuffer(vertexCountBuffer, offset: 0, index: 2)
        computeEncoder.setBytes(&params, length: MemoryLayout<ShapeShiftingSDFMarchingCubesParams>.stride, index: 3)

        let threadsPerThreadgroup = MTLSize(width: 8, height: 8, depth: 4)
        let threadgroups = MTLSize(
            width: (Int(cells.x) + threadsPerThreadgroup.width - 1) / threadsPerThreadgroup.width,
            height: (Int(cells.y) + threadsPerThreadgroup.height - 1) / threadsPerThreadgroup.height,
            depth: (Int(cells.z) + threadsPerThreadgroup.depth - 1) / threadsPerThreadgroup.depth
        )

        computeEncoder.dispatchThreadgroups(threadgroups, threadsPerThreadgroup: threadsPerThreadgroup)
        computeEncoder.endEncoding()

        commandBuffer.commit()
        commandBuffer.waitUntilCompleted()

        let vertexCount = Int(vertexCountBuffer.contents().bindMemory(to: UInt32.self, capacity: 1).pointee)
        mesh.parts.replaceAll([
            LowLevelMesh.Part(indexCount: vertexCount,
                              topology: .triangle,
                              bounds: BoundingBox(min: gridMinCornerWorldSpace, max: gridMaxCornerWorldSpace))
        ])
    }

    func randomShape(excluding: SDFShape) -> SDFShape {
        let choices = SDFShape.allCases.filter { $0 != excluding }
        return choices.randomElement()!
    }
    
    func randomizeRepetition() -> UInt32 {
        let random = Float.random(in: 0...1)
        let chance: Float = 0.25
        return random > chance ? 1 : 3
    }
}

#Preview { ShapeShiftingSDFMarchingCubesView() }

triTable.h

#ifndef triTable_h
#define triTable_h

constant int triTable[256][16] =
{{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
{3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
{9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
{8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
{3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
{4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
{5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
{9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
{0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
{10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
{5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
{9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
{2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
{11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
{11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
{9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
{2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
{6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
{6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
{6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
{3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
{10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
{10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
{1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
{0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
{10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
{3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
{6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
{10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
{7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
{0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
{7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
{2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
{7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
{2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
{10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
{7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
{6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
{6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
{8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
{1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
{10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
{10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
{9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
{7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
{6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
{6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
{9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
{1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
{0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
{5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
{11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
{2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
{1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
{9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
{5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
{8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
{9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
{11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
{1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
{4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
{3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
{0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
{1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}};

#endif /* triTable_h */

VertexPositionNormal+Extensions.swift

import Foundation
import RealityKit

extension VertexPositionNormal {
    static var vertexAttributes: [LowLevelMesh.Attribute] = [
        .init(semantic: .position, format: .float3, offset: MemoryLayout<Self>.offset(of: \.position)!),
        .init(semantic: .normal, format: .float3, offset: MemoryLayout<Self>.offset(of: \.normal)!)
    ]
    
    static var vertexLayouts: [LowLevelMesh.Layout] = [
        .init(bufferIndex: 0, bufferStride: MemoryLayout<Self>.stride)
    ]

    static var descriptor: LowLevelMesh.Descriptor {
        var desc = LowLevelMesh.Descriptor()
        desc.vertexAttributes = VertexPositionNormal.vertexAttributes
        desc.vertexLayouts = VertexPositionNormal.vertexLayouts
        desc.indexType = .uint32
        return desc
    }
    
    @MainActor static func initializeMesh(vertexCapacity: Int,
                                          indexCapacity: Int) throws -> LowLevelMesh {
        var desc = VertexPositionNormal.descriptor
        desc.vertexCapacity = vertexCapacity
        desc.indexCapacity = indexCapacity
        return try LowLevelMesh(descriptor: desc)
    }
}

VertexPositionNormal.h

#include <simd/simd.h>

#ifndef VertexPositionNormal_h
#define VertexPositionNormal_h

struct VertexPositionNormal {
    simd_float3 position;
    simd_float3 normal;
};

#endif /* VertexPositionNormal_h */