export const computeGsplatTileIntersectSource: "\n\nstruct SplatTileEval {\n    radiusFactor: f32,\n    splatMin: vec2f,\n    splatMax: vec2f,\n}\n\nfn computeRadiusFactor(opacity: half, alphaClip: f32) -> f32 {\n    return min(8.0, 2.0 * log(f32(opacity) / alphaClip));\n}\n\nfn computeSplatTileEval(\n    screen: vec2f,\n    cx: f32, cy: f32, cz: f32,\n    opacity: half,\n    viewportWidth: f32, viewportHeight: f32,\n    alphaClip: f32\n) -> SplatTileEval {\n    let K = cx * cz - cy * cy;\n    let a = 4.0 * cz / K;\n    let c = 4.0 * cx / K;\n    let radiusFactor = computeRadiusFactor(opacity, alphaClip);\n    let vmin = min(1024.0, min(viewportWidth, viewportHeight));\n    let radius = vec2f(min(sqrt(2.0 * a), vmin), min(sqrt(2.0 * c), vmin));\n    var result: SplatTileEval;\n    result.radiusFactor = radiusFactor;\n    result.splatMin = screen - radius;\n    result.splatMax = screen + radius;\n    return result;\n}\n\n// Tests if the quadratic a*t^2 + b*t + c = 0 has a root in the interval [l-d, r-d].\nfn segmentIntersectsEllipse(a: f32, b: f32, c: f32, d: f32, l: f32, r: f32) -> bool {\n    let delta = b * b - 4.0 * a * c;\n    let t1 = (l - d) * (2.0 * a) + b;\n    let t2 = (r - d) * (2.0 * a) + b;\n    return delta >= 0.0 && (t1 <= 0.0 || t1 * t1 <= delta) && (t2 >= 0.0 || t2 * t2 <= delta);\n}\n\n// Tests if the Gaussian cutoff ellipse intersects a tile rectangle.\n// Exact conic-edge intersection using positive-definite conic: cx*dx^2 + 2*cy*dx*dy + cz*dy^2 = w\nfn tileIntersectsEllipse(\n    tileMin: vec2f, tileMax: vec2f, center: vec2f,\n    cx: f32, cy: f32, cz: f32,\n    radiusFactor: f32\n) -> bool {\n    if (center.x >= tileMin.x && center.x <= tileMax.x &&\n        center.y >= tileMin.y && center.y <= tileMax.y) {\n        return true;\n    }\n\n    let w = radiusFactor;\n\n    // Test closest horizontal edge\n    var dx: f32;\n    if (center.x * 2.0 < tileMin.x + tileMax.x) {\n        dx = center.x - tileMin.x;\n    } else {\n        dx = center.x - tileMax.x;\n    }\n    if (segmentIntersectsEllipse(cz, -2.0 * cy * dx, cx * dx * dx - w, center.y, tileMin.y, tileMax.y)) {\n        return true;\n    }\n\n    // Test closest vertical edge\n    var dy: f32;\n    if (center.y * 2.0 < tileMin.y + tileMax.y) {\n        dy = center.y - tileMin.y;\n    } else {\n        dy = center.y - tileMax.y;\n    }\n    if (segmentIntersectsEllipse(cx, -2.0 * cy * dy, cz * dy * dy - w, center.x, tileMin.x, tileMax.x)) {\n        return true;\n    }\n\n    return false;\n}\n";