超雑訳 Surface Simplification Using Quadric Error Metrics

ども。Pocolです。
今日は,
[Garland 1997] Michael Garland, Paul S.Heckbert, “Surface Simplification Using Quadric Error Metrics”, SIGGRAPH 1997, pp.209-216.
を読んでみようと思います。
いつもながら誤字・誤訳があるかと思いますので,ご指摘頂ける場合は正しい翻訳例と共に指摘して頂けるとありがたいです。

(さらに…)

私的メモ:モーションブラー

A Fast and Stable Feature-Aware Motion Blur Filterの疑似コード。

float cone(float dist, float r) {
	return saturate(1.0f - abs(dist) / r);
}

float cylinder(float dist, float r) {
		return sign(r - abs(dist)) * 0.5f + 0.5f;
}

// linear depth.
float zCompare(float za, float zb) {
		const float SOFT_Z_EXTENT = 0.1f;
		return saturate(1.0 - (za - ab) / SOFT_Z_EXTENT);
}

float3 MotionBlur(float2 p)
{
	// parameter setting (see. 5. Implementation and Results).
	const auto N		= 35;	// sample count.
	const auto eta		= 0.95; // a larger maximum jitter value (in pixel units). (see p.6)
	const auto phi		= 27;	// user-determined constant which affects the "baseline2 jitter level. (see p.6)
	const auto kappa	= 40;	// use-parameter to bais its importance. (see p.6)
	const auto r		= 40;	// a maximum image-space blur radius. (see p.2)
	const auto gamma	= 1.5;	// minimum user threshold (see p.4)

	auto j = Halton(-1, 1);

	// sOffset jitters a tile lookup (but never into a diagonal tile).
	auto vmax = FetchNeighborMax(p/r + sOffset(p, j));
	auto mag_vmax = length(vmax);
	if (mag_vmax <= 0.5f)
	{
		return FetchColor(p);
	}

	auto wn = vmax / mag_vmax;
	auto vc = FetchVelocity(p);
	auto wp = (-wn.y, wn.x); // vmax⊥.

	if (dot(wp, vc) < 0.0)
	{
		wp = -wp;
	}

	auto mag_vc = length(vc);
	auto wc = normalize(lerp(normalize(vc), wp, (mag_vc - 0.5) / gamma); // Eq. (1).

	// First integration samples: p with center weight
	auto totalWeight = N / (kappa * mag_vc);
	auto result = FetchColor(p) * totalWeight;
	auto j_dash = j * eta * phi / N;

	auto z_p = FetchDepth(p);

	for(int i=0; i<N; ++i)
	{
		auto t = lerp(-1.0, 1.0, (i+j_dash + 1)/(N+1)); // jitter sampler

		// Compute point S; split samples between {vmax, vc}
		auto d = (i & 0x1) ? vc : vmax; // iが奇数なら vc, iが偶数なら vmax.
		auto T = t * mag_vmax;
		auto S = int2(t * d) + p;

		// Compute S's velocity and color
		auto vs = FetchVelocity(S);
		auto colorSmaple = FetchColor(S);

		auto z_S = FetchDepth(S);

		// Fore-vs. background classification Y w.r.t p
		auto f = zCompare(z_p, z_S);
		auto b = zCompare(z_S, z_p);

		// Sample weight and velocity-aware factors (Sec.4.1)
		// The length of v_s is clamped to 0.5 minimum during normalization
		auto weight = 0;
		auto wA = dot(wc, d);
		auto wB = dot(normalize(vs), d);

		auto mag_vs = length(vs);

		// 3 phenomenological cases (Sec. 3, 4.1): Object
		// moving over p, p's blurred motion, & their blending.
		weight += dot(f, cone(T, 1 / mag_vs)) * wB;
		weight += dot(b, cone(T, 1 / mag_vc)) * wA;
		weight += cylinder(T, min(mag_vs, mag_vc)) * max(wA, wB) * 2;

		totalWeight += weight; // For normalization
		result += colorSample * weight;
	}

	return result / totalWeight;
}

McGuireのG3Dエンジンでは論文実装よりも変更がある。以下のように内積計算部分がガッツリなくなっている。
https://sourceforge.net/p/g3d/code/HEAD/tree/G3D10/data-files/shader/MotionBlur/MotionBlur_gather.pix

auto f = zCompare(z_p, z_S);
auto b = zCompare(z_S, z_p);

auto weight = 0.0f;
weight += b * cone(T, 1 / mag_vs);
weight += f * cone(T, 1 / mag_vc);
weight += cylinder(T, min(mag_vs, mag_vc)) * 2.0f;

totalWeight += weight;
result += colorSample * weight;