fix normalization

src/lib.rs

@@ -328,7 +328,7 @@ impl Core {
 		}
 		let light_at = {
 			let sigma2 = args.accum_sigma.powi(2);
-			let accum_normalizator = (2. * PI * sigma2).sqrt().recip();
+			let accum_normalizator = (2. * PI * sigma2).recip();
 			let hits = &hits;
 			move |hit: Hit| -> f32 {
 				let mut total_cd = 0.0f32;
@@ -384,7 +384,7 @@ impl Core {
 		if args.show_shapes {
 			let mut meshes = Vec::new();
 			for obj in &scene.objects {
-				let mesh = shape::sphere((obj.radius * 45.) as usize + 7);
+				let mesh = shape::octo_sphere((obj.radius * 45.) as usize + 7);
 				let obj_mesh = render::faces::Mesh::new(
 					&self.device,
 					&mesh

src/shape.rs

@@ -60,6 +60,114 @@ pub fn sphere(subdiv: usize) -> Mesh {
 	Mesh { vertices, indices }
 }
 
+pub fn octo_sphere(subdiv: usize) -> Mesh {
+	assert!(subdiv >= 2);
+
+	let mut vertices = Vec::new();
+	let theta_step = PI / subdiv as f32;
+	let v_belt = |j: usize, n: usize| {
+		let phi_step = 2. * PI / n as f32;
+		let theta = j as f32 * theta_step;
+		let (xy, z) = theta.sin_cos();
+		(0..n).map(move |i| {
+			let phi = i as f32 * phi_step;
+			let (y, x) = phi.sin_cos();
+			vec3(xy * x, xy * y, z)
+		})
+	};
+	vertices.push(Vec3::Z);
+	for j in 1..subdiv / 2 {
+		vertices.extend(v_belt(j, 4 * j));
+	}
+	{
+		let j = subdiv / 2;
+		vertices.extend(v_belt(j, 4 * j));
+	}
+	for j in (subdiv + 2) / 2..subdiv {
+		vertices.extend(v_belt(j, 4 * (subdiv - j)));
+	}
+	vertices.push(-Vec3::Z);
+
+	fn i_cap(top: usize, start: usize) -> impl Iterator<Item = Face> {
+		gen move {
+			yield [top, start, start + 1];
+			yield [top, start + 1, start + 2];
+			yield [top, start + 2, start + 3];
+			yield [top, start + 3, start];
+		}
+		.map(face)
+	}
+	fn i_skew_belt(
+		short_start: usize,
+		long_start: usize,
+		seg_short_face: usize,
+	) -> impl Iterator<Item = Face> {
+		gen move {
+			let seg_long_face = seg_short_face + 1;
+			let n_short_total = 4 * seg_short_face;
+			let n_long_total = 4 * seg_long_face;
+			for face in 0..4 {
+				let short = move |k| short_start + (face * seg_short_face + k) % n_short_total;
+				let long = move |k| long_start + (face * seg_long_face + k) % n_long_total;
+				yield [short(0), long(0), long(1)];
+				for k in 0..seg_short_face {
+					yield [short(k), long(k + 1), short(k + 1)];
+					yield [short(k + 1), long(k + 1), long(k + 2)];
+				}
+			}
+		}
+		.map(face)
+	}
+	fn i_belt(start1: usize, start2: usize, seg_per_face: usize) -> impl Iterator<Item = Face> {
+		gen move {
+			let n = 4 * seg_per_face;
+			for k in 0..n {
+				let k2 = (k + 1) % n;
+				let a = start1 + k;
+				let b = start2 + k;
+				let c = start1 + k2;
+				let d = start2 + k2;
+				yield [a, b, c];
+				yield [c, b, d];
+			}
+		}
+		.map(face)
+	}
+	fn face(f: [usize; 3]) -> Face {
+		f.map(|i| i as u16)
+	}
+	fn flip(f: Face) -> Face {
+		[f[1], f[0], f[2]]
+	}
+
+	let mut indices = Vec::new();
+	indices.extend(i_cap(0, 1));
+	let mut k = 1;
+	for j in 1..subdiv - 1 {
+		let j2 = (subdiv - 1) - j;
+		match j.cmp(&j2) {
+			std::cmp::Ordering::Less => {
+				let n = 4 * j;
+				indices.extend(i_skew_belt(k, k + n, j));
+				k += n;
+			}
+			std::cmp::Ordering::Equal => {
+				let n = 4 * j;
+				indices.extend(i_belt(k, k + n, j));
+				k += n;
+			}
+			std::cmp::Ordering::Greater => {
+				let n = 4 * (j2 + 1);
+				indices.extend(i_skew_belt(k + n, k, j2).map(flip));
+				k += n;
+			}
+		}
+	}
+	indices.extend(i_cap(k + 4, k).map(flip));
+
+	Mesh { vertices, indices }
+}
+
 #[cfg(test)]
 mod tests {
 	use approx::abs_diff_eq;
@@ -137,4 +245,104 @@ mod tests {
 			]
 		);
 	}
+
+	#[test]
+	fn test_octo_sphere_2_topology() {
+		assert_eq!(
+			octo_sphere(2).indices,
+			vec![
+				[0, 1, 2],
+				[0, 2, 3],
+				[0, 3, 4],
+				[0, 4, 1],
+				[1, 5, 2],
+				[2, 5, 3],
+				[3, 5, 4],
+				[4, 5, 1],
+			]
+		);
+	}
+
+	#[test]
+	fn test_octo_sphere_2_geometry() {
+		let left = octo_sphere(2).vertices;
+		let right = [Vec3::Z, Vec3::X, Vec3::Y, -Vec3::X, -Vec3::Y, -Vec3::Z];
+		assert!(
+			are_equal_eps(&left, &right, 1e-6),
+			"assertion `left == right` failed\n  left: {left:?}\n right: {right:?}"
+		);
+	}
+
+	#[test]
+	fn test_octo_sphere_3_topology() {
+		assert_eq!(
+			octo_sphere(3).indices,
+			vec![
+				// top
+				[0, 1, 2],
+				[0, 2, 3],
+				[0, 3, 4],
+				[0, 4, 1],
+				// belt
+				[1, 5, 2],
+				[2, 5, 6],
+				[2, 6, 3],
+				[3, 6, 7],
+				[3, 7, 4],
+				[4, 7, 8],
+				[4, 8, 1],
+				[1, 8, 5],
+				// bottom
+				[5, 9, 6],
+				[6, 9, 7],
+				[7, 9, 8],
+				[8, 9, 5],
+			]
+		);
+	}
+
+	#[test]
+	fn test_octo_sphere_4_topology() {
+		assert_eq!(
+			octo_sphere(4).indices,
+			vec![
+				// top
+				[0, 1, 2],
+				[0, 2, 3],
+				[0, 3, 4],
+				[0, 4, 1],
+				// belt 1
+				[1, 5, 6],
+				[1, 6, 2],
+				[2, 6, 7],
+				[2, 7, 8],
+				[2, 8, 3],
+				[3, 8, 9],
+				[3, 9, 10],
+				[3, 10, 4],
+				[4, 10, 11],
+				[4, 11, 12],
+				[4, 12, 1],
+				[1, 12, 5],
+				// belt 2
+				[5, 13, 6],
+				[6, 13, 14],
+				[6, 14, 7],
+				[7, 14, 8],
+				[8, 14, 15],
+				[8, 15, 9],
+				[9, 15, 10],
+				[10, 15, 16],
+				[10, 16, 11],
+				[11, 16, 12],
+				[12, 16, 13],
+				[12, 13, 5],
+				// bottom
+				[13, 17, 14],
+				[14, 17, 15],
+				[15, 17, 16],
+				[16, 17, 13],
+			]
+		);
+	}
 }

ui/src/main_window.cxx

@@ -52,8 +52,8 @@ void PhotonLight::updateView() {
 	m_ui->lightYawLabel->setText(tr("Yaw: %1 deg").arg(QString::number(qRadiansToDegrees(args.light_position.yaw))));
 	m_ui->lightPitchLabel->setText(tr("Pitch: %1 deg").arg(QString::number(qRadiansToDegrees(args.light_position.pitch))));
 	m_ui->lightDistanceLabel->setText(tr("Distance: %1").arg(QString::number(args.light_position.distance)));
-	m_ui->accumSigmaLabel->setText(tr("Averaging radius: %1").arg(QString::number(args.accum_sigma, 'f', 3)));
+	m_ui->accumSigmaLabel->setText(tr("Averaging radius: %1").arg(QString::number(args.accum_sigma, 'f', 5)));
-	m_ui->accumScaleLabel->setText(tr("Brightness: %1").arg(QString::number(args.accum_scale, 'f', 3)));
+	m_ui->accumScaleLabel->setText(tr("Brightness: %1").arg(QString::number(args.accum_scale, 'f', 5)));
 	m_ui->viewport->setView(args);
 }
 

ui/src/main_window.ui

@@ -245,7 +245,7 @@
            <number>0</number>
           </property>
           <property name="value">
-           <number>-40</number>
+           <number>-45</number>
           </property>
           <property name="orientation">
            <enum>Qt::Horizontal</enum>
@@ -271,7 +271,7 @@
            <number>0</number>
           </property>
           <property name="value">
-           <number>-50</number>
+           <number>-85</number>
           </property>
           <property name="orientation">
            <enum>Qt::Horizontal</enum>