Signed Distance Field in Metal/Swift

FontAtlas.swift

public class FontAtlas: NSObject, NSSecureCoding {
    public static var supportsSecureCoding: Bool { get { return true } }

    static let atlasSize: Int = 2048 // 4096 runs out of mem...
    var glyphs : [GlyphDescriptor] = []
    let parentFont: UIFont
    var fontPointSize: CGFloat
    let textureSize: Int
    var textureData: [UInt8] = []
  
    /// Compute signed-distance field for an 8-bpp grayscale image (values greater than 127 are considered "on")
    /// For details of this algorithm, see "The 'dead reckoning' signed distance transform" [Grevera 2004]
    private func createSignedDistanceFieldForGrayscaleImage(imageData: UnsafeMutablePointer<UInt8>, width: Int, height: Int) -> [Float] {
        let maxDist = hypot(Float(width), Float(height))
        // Initialization phase
        // distance to nearest boundary point map - set all distances to "infinity"
        var distanceMap = [Float](repeating: maxDist, count: width * height)
        // nearest boundary point map - zero out nearest boundary point map
        var boundaryPointMap = [int2](repeating: int2(0,0), count: width * height)
        let distUnit :Float = 1
        let distDiag :Float = sqrtf(2)
        // Immediate interior/exterior phase: mark all points along the boundary as such
        for y in 1..<(height-1) {
            for x in 1..<(width-1) {
                let inside = imageData[y * width + x] > 0x7f
                if (imageData[y * width + x - 1] > 0x7f) != inside
                    || (imageData[y * width + x + 1] > 0x7f) != inside
                    || (imageData[(y - 1) * width + x] > 0x7f) != inside
                    || (imageData[(y + 1) * width + x] > 0x7f) != inside {
                    distanceMap[y * width + x] = 0
                    boundaryPointMap[y * width + x].x = Int32(x)
                    boundaryPointMap[y * width + x].y = Int32(y)
                }
            }
        }
        // Forward dead-reckoning pass
        for y in 1..<(height-2) {
            for x in 1..<(width-2) {
                let d = distanceMap[y * width + x]
                let n = boundaryPointMap[y * width + x]
                let h = hypot(Float(x) - Float(n.x), Float(y) - Float(n.y))
                if distanceMap[(y - 1) * width + x - 1] + distDiag < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[(y - 1) * width + (x - 1)]
                    distanceMap[y * width + x] = h
                }
                if distanceMap[(y - 1) * width + x] + distUnit < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[(y - 1) * width + x]
                    distanceMap[y * width + x] = h
                }
                if distanceMap[(y - 1) * width + x + 1] + distDiag < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[(y - 1) * width + (x + 1)]
                    distanceMap[y * width + x] = h
                }
                if distanceMap[y * width + x - 1] + distUnit < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[y * width + (x - 1)]
                    distanceMap[y * width + x] = h
                }
            }
        }
        // Backward dead-reckoning pass
        for y in (1...(height-2)).reversed() {
            for x in (1...(width-2)).reversed() {
                let d = distanceMap[y * width + x]
                let n = boundaryPointMap[y * width + x]
                let h = hypot(Float(x) - Float(n.x), Float(y) - Float(n.y))
                if distanceMap[y * width + x + 1] + distUnit < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[y * width + x + 1]
                    distanceMap[y * width + x] = h
                }
                if distanceMap[(y + 1) * width + x - 1] + distDiag < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[(y + 1) * width + x - 1]
                    distanceMap[y * width + x] = h
                }
                if distanceMap[(y + 1) * width + x] + distUnit < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[(y + 1) * width + x]
                    distanceMap[y * width + x] = h
                }
                if distanceMap[(y + 1) * width + x + 1] + distDiag < d {
                    boundaryPointMap[y * width + x] = boundaryPointMap[(y + 1) * width + x + 1]
                    distanceMap[y * width + x] = h
                }
            }
        }
        // Interior distance negation pass; distances outside the figure are considered negative
        for y in 0..<height {
            for x in 0..<width {
                if imageData[y * width + x] <= 0x7f {
                    distanceMap[y * width + x] = -distanceMap[y * width + x]
                }
            }
        }
        return distanceMap
    }
  
    // ...
  }