Cycles: add offscreen dicing scale and dicing camera.

The offscreen dicing scale helps to significantly reduce memory usage,
by reducing the dicing rate for objects the further they are outside of
the camera view.

The dicing camera can be specified now, to keep the geometry fixed and
avoid crawling artifacts in animation. It is also useful for debugging,
to see the tesselation from a different camera location.

Differential Revision: https://developer.blender.org/D2891

intern/cycles/render/camera.cpp

@@ -128,6 +128,8 @@ NODE_DEFINE(Camera)
 	SOCKET_FLOAT(border.bottom, "Border Bottom", 0);
 	SOCKET_FLOAT(border.top, "Border Top", 0);
 
+	SOCKET_FLOAT(offscreen_dicing_scale, "Offscreen Dicing Scale", 1.0f);
+
 	return type;
 }
 
@@ -273,6 +275,13 @@ void Camera::update()
 	full_dx = transform_direction(&cameratoworld, full_dx);
 	full_dy = transform_direction(&cameratoworld, full_dy);
 
+	if(type == CAMERA_PERSPECTIVE) {
+		float3 v = transform_perspective(&full_rastertocamera, make_float3(full_width, full_height, 1.0f));
+
+		frustum_right_normal = normalize(make_float3(v.z, 0.0f, -v.x));
+		frustum_top_normal = normalize(make_float3(0.0f, v.z, -v.y));
+	}
+
 	/* TODO(sergey): Support other types of camera. */
 	if(type == CAMERA_PERSPECTIVE) {
 		/* TODO(sergey): Move to an utility function and de-duplicate with
@@ -581,8 +590,27 @@ BoundBox Camera::viewplane_bounds_get()
 
 float Camera::world_to_raster_size(float3 P)
 {
+	float res = 1.0f;
+
 	if(type == CAMERA_ORTHOGRAPHIC) {
-		return min(len(full_dx), len(full_dy));
+		res = min(len(full_dx), len(full_dy));
+
+		if(offscreen_dicing_scale > 1.0f) {
+			float3 p = transform_perspective(&worldtocamera, P);
+			float3 v = transform_perspective(&rastertocamera, make_float3(width, height, 0.0f));
+
+			/* Create point clamped to frustum */
+			float3 c;
+			c.x = max(-v.x, min(v.x, p.x));
+			c.y = max(-v.y, min(v.y, p.y));
+			c.z = max(0.0f, p.z);
+
+			float f_dist = len(p - c) / sqrtf((v.x*v.x+v.y*v.y)*0.5f);
+
+			if(f_dist > 0.0f) {
+				res += res * f_dist * (offscreen_dicing_scale - 1.0f);
+			}
+		}
 	}
 	else if(type == CAMERA_PERSPECTIVE) {
 		/* Calculate as if point is directly ahead of the camera. */
@@ -597,14 +625,74 @@ float Camera::world_to_raster_size(float3 P)
 		/* dPdx */
 		float dist = len(transform_point(&worldtocamera, P));
 		float3 D = normalize(Ddiff);
-		return len(dist*dDdx - dot(dist*dDdx, D)*D);
+		res = len(dist*dDdx - dot(dist*dDdx, D)*D);
+
+		/* Decent approx distance to frustum (doesn't handle corners correctly, but not that big of a deal) */
+		float f_dist = 0.0f;
+
+		if(offscreen_dicing_scale > 1.0f) {
+			float3 p = transform_point(&worldtocamera, P);
+
+			/* Distance from the four planes */
+			float r = dot(p, frustum_right_normal);
+			float t = dot(p, frustum_top_normal);
+			p = make_float3(-p.x, -p.y, p.z);
+			float l = dot(p, frustum_right_normal);
+			float b = dot(p, frustum_top_normal);
+			p = make_float3(-p.x, -p.y, p.z);
+
+			if(r <= 0.0f && l <= 0.0f && t <= 0.0f && b <= 0.0f) {
+				/* Point is inside frustum */
+				f_dist = 0.0f;
+			}
+			else if(r > 0.0f && l > 0.0f && t > 0.0f && b > 0.0f) {
+				/* Point is behind frustum */
+				f_dist = len(p);
+			}
+			else {
+				/* Point may be behind or off to the side, need to check */
+				float3 along_right = make_float3(-frustum_right_normal.z, 0.0f, frustum_right_normal.x);
+				float3 along_left = make_float3(frustum_right_normal.z, 0.0f, frustum_right_normal.x);
+				float3 along_top = make_float3(0.0f, -frustum_top_normal.z, frustum_top_normal.y);
+				float3 along_bottom = make_float3(0.0f, frustum_top_normal.z, frustum_top_normal.y);
+
+				float dist[] = {r, l, t, b};
+				float3 along[] = {along_right, along_left, along_top, along_bottom};
+
+				bool test_o = false;
+
+				float *d = dist;
+				float3 *a = along;
+				for(int i = 0; i < 4; i++, d++, a++) {
+					/* Test if we should check this side at all */
+					if(*d > 0.0f) {
+						if(dot(p, *a) >= 0.0f) {
+							/* We are in front of the back edge of this side of the frustum */
+							f_dist = max(f_dist, *d);
+						}
+						else {
+							/* Possibly far enough behind the frustum to use distance to origin instead of edge */
+							test_o = true;
+						}
+					}
+				}
+
+				if(test_o) {
+					f_dist = (f_dist > 0) ? min(f_dist, len(p)) : len(p);
+				}
+			}
+
+			if(f_dist > 0.0f) {
+				res += len(dDdx - dot(dDdx, D)*D) * f_dist * (offscreen_dicing_scale - 1.0f);
+			}
+		}
 	}
 	else {
 		// TODO(mai): implement for CAMERA_PANORAMA
 		assert(!"pixel width calculation for panoramic projection not implemented yet");
 	}
 
-	return 1.0f;
+	return res;
 }
 
 CCL_NAMESPACE_END