private static float max_error_location(Arc arc, float begin_point_angle, float end_point_angle)
{
OctahedronUVCoordinates begin_point = new NormalizedCartesianCoordinates(arc.position(begin_point_angle));
OctahedronUVCoordinates end_point = new NormalizedCartesianCoordinates(arc.position(end_point_angle));
float begin = begin_point_angle;
float end = end_point_angle;
// 2) use binary / bisection search to find the point of maximal error
while (end - begin > Precision.delta)
{
float midpoint = (begin + end) / 2;
OctahedronUVCoordinates left_midpoint = new NormalizedCartesianCoordinates(arc.position(midpoint - Precision.delta));
OctahedronUVCoordinates right_midpoint = new NormalizedCartesianCoordinates(arc.position(midpoint + Precision.delta));
float error_left = PlanetariaMath.point_line_distance(begin_point.data, end_point.data, left_midpoint.data);
float error_right = PlanetariaMath.point_line_distance(begin_point.data, end_point.data, right_midpoint.data);
if (error_left < error_right) //error begin should be replaced since it has less error
{
begin = midpoint;
}
else //error end should be replaced since it has less error
{
end = midpoint;
}
}
return((begin + end) / 2); // return location of max error
}
public Discontinuity(Arc arc, NormalizedCartesianCoordinates position)
{
this.arc = arc;
this.position = position.data;
this.angle = arc.position_to_angle(this.position);
Debug.Assert(Mathf.Abs(angle) <= arc.angle() / 2);
}
public override void step()
{
NormalizedSphericalCoordinates self_position = new NormalizedCartesianCoordinates(self.position);
NormalizedSphericalCoordinates target_position = new NormalizedCartesianCoordinates(target.position);
NormalizedCartesianCoordinates next_position = new NormalizedSphericalCoordinates(self_position.elevation, target_position.azimuth);
self.position = next_position.data;
}
private static void add_intersection(Arc arc, NormalizedCartesianCoordinates position)
{
if (position.data.y <= 0) // FIXME:
{
if (!discontinuities.ContainsKey(arc))
{
discontinuities.Add(arc, new List <Discontinuity>());
}
discontinuities[arc].Add(new Discontinuity(arc, position));
}
}
public PointPlanetarium(Vector3 point, float radius)
{
this.point = point;
this.radius = radius;
// cache for early return
Vector3 furthest_point = Vector3.RotateTowards(point, -point, radius, 0.0f);
dot_product_threshold = Vector3.Dot(point, furthest_point);
pixel_centroids = new NormalizedCartesianCoordinates[0];
}
private static Vector3 grid_snap(Vector3 position) // FIXME: optimize
{
if (!Event.current.shift) // only snap when shift key is held
{
return(position);
}
NormalizedCartesianCoordinates cartesian_position = new NormalizedCartesianCoordinates(position);
NormalizedSphericalCoordinates clamped_coordinates = new NormalizedSphericalCoordinates(0, 0);
NormalizedSphericalCoordinates desired_coordinates = cartesian_position;
for (float row = 0; row <= EditorGlobal.self.rows + 1; ++row) //going over with off by one errors won't ruin the program...
{
float angle = Mathf.PI * row / (EditorGlobal.self.rows + 1); // TODO: verify the row/columns are not swapped
float x = Mathf.Sin(angle);
float y = Mathf.Cos(angle);
NormalizedSphericalCoordinates test_coordinates = new NormalizedCartesianCoordinates(new Vector3(x, y, 0));
float error = Mathf.Abs(Mathf.DeltaAngle(desired_coordinates.elevation * Mathf.Rad2Deg, test_coordinates.elevation * Mathf.Rad2Deg));
float old_error = Mathf.Abs(Mathf.DeltaAngle(desired_coordinates.elevation * Mathf.Rad2Deg, clamped_coordinates.elevation * Mathf.Rad2Deg));
if (error < old_error)
{
clamped_coordinates = new NormalizedSphericalCoordinates(test_coordinates.elevation, clamped_coordinates.azimuth);
}
}
for (float column = 0; column < EditorGlobal.self.columns * 2; ++column) //... but going under is bad
{
float angle = column / EditorGlobal.self.columns * Mathf.PI;
float x = Mathf.Sin(angle);
float z = Mathf.Cos(angle);
NormalizedSphericalCoordinates test_coordinates = new NormalizedCartesianCoordinates(new Vector3(x, 0, z));
float error = Mathf.Abs(Mathf.DeltaAngle(desired_coordinates.azimuth * Mathf.Rad2Deg, test_coordinates.azimuth * Mathf.Rad2Deg));
float old_error = Mathf.Abs(Mathf.DeltaAngle(desired_coordinates.azimuth * Mathf.Rad2Deg, clamped_coordinates.azimuth * Mathf.Rad2Deg));
if (error < old_error)
{
clamped_coordinates = new NormalizedSphericalCoordinates(clamped_coordinates.elevation, test_coordinates.azimuth);
}
}
cartesian_position = clamped_coordinates;
return(cartesian_position.data);
}
public ArcPlanetarium(Arc arc, float radius)
{
this.arc = arc;
this.radius = radius;
// cache for early return
center = arc.position(0);
Vector3 vertex = arc.position(arc.angle() / 2);
Vector3 furthest_point = Vector3.RotateTowards(vertex, -center, radius, 0.0f);
dot_product_threshold = Vector3.Dot(center, furthest_point);
SphericalCap lower = arc.floor(-radius);
SphericalCap upper = arc.floor(+radius);
center_offset = lower.offset + upper.offset;
center_range = Mathf.Abs(upper.offset - lower.offset) / 2;
pixel_centroids = new NormalizedCartesianCoordinates[0];
}
private static void subdivide(Arc arc, float begin_point_angle, float end_point_angle)
{
float middle_point_angle = max_error_location(arc, begin_point_angle, end_point_angle);
Vector3 begin = arc.position(begin_point_angle);
Vector3 middle = arc.position(middle_point_angle);
Vector3 end = arc.position(end_point_angle);
OctahedronUVCoordinates begin_point = new NormalizedCartesianCoordinates(begin);
OctahedronUVCoordinates middle_point = new NormalizedCartesianCoordinates(middle);
OctahedronUVCoordinates end_point = new NormalizedCartesianCoordinates(end);
if (PlanetariaMath.point_line_distance(begin_point.data, end_point.data, middle_point.data) > Precision.threshold) // if the max error is greater than a threshold, recursively add the left and right halves into the list of lines
{
subdivide(arc, begin_point_angle, middle_point_angle);
subdivide(arc, middle_point_angle, end_point_angle);
}
else
{
QuadraticBezierCurve curve = new QuadraticBezierCurve(begin_point.data, middle_point.data, end_point.data);
VectorGraphicsWriter.set_edge(curve);
}
}
protected override void initialize()
{
Camera camera = this.GetComponentInChildren <Camera>() as Camera;
shutter_edges = new GameObject[edges];
for (int edge_index = 0; edge_index < edges; ++edge_index)
{
shutter_edges[edge_index] = (GameObject)Instantiate(Resources.Load("PrimaryEdge"),
new Vector3(0, 0, 2 * PlanetariaCamera.near_clip_plane),
Quaternion.Euler(0, 0, edge_index * 360f / edges), camera.transform);
#if UNITY_EDITOR
shutter_edges[edge_index].transform.localScale = Vector3.one * 4 * PlanetariaMath.cone_radius(2 * PlanetariaCamera.near_clip_plane, camera.fieldOfView * Mathf.Deg2Rad) * Mathf.Sqrt(1 + (camera.aspect * camera.aspect));
#else
float x = PlanetariaMath.cone_radius(2 * PlanetariaCamera.near_clip_plane, camera.fieldOfView * Mathf.Deg2Rad);
float y = x * camera.aspect;
float z = 2 * PlanetariaCamera.near_clip_plane;
StereoscopicProjectionCoordinates stereoscopic_projection = new NormalizedCartesianCoordinates(new Vector3(x, y, z));
shutter_edges[edge_index].transform.localScale = Vector3.one * stereoscopic_projection.data.magnitude; // FIXME: VR FOV
#endif
}
}
public NormalizedCartesianCoordinates TransformDirection(NormalizedCartesianCoordinates local_space)
{
return((NormalizedCartesianCoordinates)internal_transform.TransformDirection(local_space.data));
}
public NormalizedCartesianCoordinates InverseTransformDirection(NormalizedCartesianCoordinates world_space)
{
return((NormalizedCartesianCoordinates)internal_transform.InverseTransformDirection(world_space.data));
}
