// Preview rendering of this function is non-trivial, since ephemeral edges only work for the most recent edge.
public static PlanetariaShape create_equilateral(PlanetariaShape shape, Vector3 center, Vector3 vertex, int faces,
PlanetariaShape.AppendMode permanence = PlanetariaShape.AppendMode.OverwriteWithPermanent)
{
if (faces > 0 && center != vertex)
{
if (faces >= 2)
{
Vector3 forward = center.normalized;
Vector3 right = Vector3.ProjectOnPlane(vertex, forward).normalized;
Vector3 up = Vector3.Cross(forward, right).normalized;
float phi = Vector3.Angle(vertex, center) * Mathf.Deg2Rad;
List <Vector3> vertices = new List <Vector3>();
for (float face_index = 0; face_index < faces; ++face_index)
{
Vector3 equatorial_position = PlanetariaMath.spherical_linear_interpolation(right, up, -(face_index / faces) * (Mathf.PI * 2));
Vector3 final_position = PlanetariaMath.spherical_linear_interpolation(forward, equatorial_position, phi);
vertices.Add(final_position);
}
List <SerializedArc> polygon = new List <SerializedArc>();
for (int face_index = 0; face_index < faces; ++face_index)
{
Vector3 start_point = vertices[face_index];
Vector3 end_point = vertices[(face_index + 1) % faces];
polygon.Add(ArcFactory.line(start_point, end_point));
}
shape.append(polygon, permanence);
return(shape);
}
else // create a circle with given radius
{
// first_vertex is circle start
Vector3 right = Vector3.Cross(center, vertex).normalized;
Vector3 mirror = Vector3.Cross(center, right).normalized;
Vector3 hidden_vertex = Vector3.Reflect(vertex, mirror).normalized; // opposite end of circle start
Vector3 first_up = Vector3.Cross(vertex, right).normalized;
Vector3 first_tangent = -Vector3.Cross(first_up, vertex).normalized;
Vector3 second_up = -Vector3.Cross(hidden_vertex, right).normalized;
Vector3 second_tangent = -Vector3.Cross(second_up, hidden_vertex).normalized;
SerializedArc upper_circle = ArcFactory.curve(vertex, first_tangent, hidden_vertex);
SerializedArc lower_circle = ArcFactory.curve(hidden_vertex, second_tangent, vertex);
// TODO: this entire function can be replaced now (with the circle generator)
shape.append(new List <SerializedArc>()
{
upper_circle, lower_circle
}, permanence);
return(shape);
}
}
shape.append(new List <SerializedArc>(), permanence);
return(shape);
}
/// <summary>
/// Inspector - Finds the collision points between an arc extrapolated to be distance long (the PlanetariaRaycastHit structs have no particular order)
/// </summary>
/// <param name="arc">A fragment that defines the arc in space (might not be fully used or return collisions after the end of the arc).</param>
/// <param name="distance">The distance to raycast (may be greater than or less than the length of the arc - or negative).</param>
/// <param name="layer_mask">The collision mask that defines which objects will be ignored.</param>
/// <returns>All of the collision points of the Raycast (listed exactly once).</returns>
private static PlanetariaRaycastHit[] unordered_raycast_all(Arc arc, float distance, int layer_mask, bool collide_with_fields)
{
//float angle = arc.angle(); // this would determine the intersections for the un-modified arc (ignoring distance)
// desired_angle = desired_length * (partial_angle/partial_length) i.e. length * length_to_angle ratio
float desired_angle = distance * (arc.angle() / arc.length()); // TODO: verify negative distances go backwards
desired_angle = Mathf.Clamp(desired_angle, -2 * Mathf.PI, 2 * Mathf.PI);
// primative arc points
Vector3 arc_left = arc.position(-arc.angle() / 2);
Vector3 arc_center = arc.position(-arc.angle() / 2 + desired_angle / 2);
Vector3 arc_right = arc.position(-arc.angle() / 2 + desired_angle);
SerializedArc ray_arc = ArcFactory.curve(arc_left, arc_center, arc_right);
PlanetariaShape ray_shape = PlanetariaShape.Create(new List <SerializedArc> {
ray_arc
}, false);
// composites
Vector3 arc_boundary_midpoint = (arc_left + arc_right) / 2; // if the arc is like a wooden bow, this is the midpoint of the string
Vector3 arc_forward = (arc_center - arc_boundary_midpoint).normalized; // the direction a hypothetical arrow would travel
Vector3 arc_up = arc.floor().normal; // orthogonal/perpendicular to the imaginary "bow"
// UnityEngine.Physics.OverlapBox() requirements
// FIXME: OPTIMIZE: half_extents currently provides unnecessary false positives because the "width" of plane (the depth into the distance and zero height are fine)
Vector3 half_extents = new Vector3(1, 0, 1); // The largest collision "box" for a unit sphere is a radius of 1 in the x-z plane; height along y is 0.
Vector3 center = arc_boundary_midpoint + arc_forward * 1; // The center of the "box" must be offset 1 (the radius) along the forward axis from the two arc boundaries.
Quaternion rotation = Quaternion.LookRotation(arc_forward, arc_up);
// SphereColliders (only) that represent potential collisions (not guaranteed).
Collider[] colliders = Physics.OverlapBox(center, half_extents, rotation, layer_mask, QueryTriggerInteraction.Collide); // TODO: verify this casts properly
List <PlanetariaRaycastHit> raycast_hits = new List <PlanetariaRaycastHit>();
Debug.Log(colliders.Length);
foreach (SphereCollider sphere_collider in colliders)
{
PlanetariaCollider planetaria_collider = PlanetariaCache.collider_fetch(sphere_collider);
if (planetaria_collider.is_field && !collide_with_fields)
{
Debug.LogError("Why?");
continue;
}
Quaternion geometry_rotation = planetaria_collider.gameObject.internal_game_object.transform.rotation;
Debug.Log("Found a collider with " + planetaria_collider.shape.Length + " arcs.");
foreach (Arc geometry_arc in ray_shape.block_collision(planetaria_collider.shape, geometry_rotation))
{
Vector3[] intersections = PlanetariaIntersection.raycast_intersection(arc, geometry_arc, distance, geometry_rotation); // TODO: verify distance is indeed the angle in this scenario
Debug.Log("Found an arc with " + intersections.Length + " intersections.");
foreach (Vector3 intersection in intersections)
{
PlanetariaRaycastHit single_collision = PlanetariaRaycastHit.hit(arc, planetaria_collider, geometry_arc, intersection, distance);
raycast_hits.Add(single_collision);
}
}
}
return(raycast_hits.ToArray());
}
private static Vector3 intersection(float longitude, float latitude) // FIXME: Rect canvas
{
Arc x_boundary = ArcFactory.curve(Vector3.down, equator_longitude(longitude), Vector3.up); // full-circle
Arc y_boundary = ArcFactory.curve(Vector3.left, prime_meridian_latitude(latitude), Vector3.left); // semi-circle
Vector3 corner = PlanetariaIntersection.arc_arc_intersection(x_boundary, y_boundary, 0).data;
return(corner);
}
private static Arc boundary(Vector2 start_longitude_latitude, Vector2 end_longitude_latitude)
{
Vector3 first_corner = intersection(start_longitude_latitude.x, start_longitude_latitude.y);
Vector3 end_corner = intersection(end_longitude_latitude.x, end_longitude_latitude.y);
Vector2 middle_longitude_latitude = (start_longitude_latitude + end_longitude_latitude) / 2;
Vector3 axis = intersection(middle_longitude_latitude.x, middle_longitude_latitude.y);
return(ArcFactory.curve(first_corner, axis, end_corner));
}
public void next()
{
if (state == CreationState.SetPoint)
{
shape.append(ArcFactory.curve(previous_point, slope, point));
previous_point = point;
}
state = (state == CreationState.SetSlope ? CreationState.SetPoint : CreationState.SetSlope); // state = !state;
}
public void receive_vector(Vector3 vector)
{
if (state == CreationState.SetSlope)
{
slope = vector;
shape.append(ArcFactory.line(point, slope), PlanetariaShape.AppendMode.OverwriteWithEphemeral);
}
else // CreationState.SetPoint
{
point = vector;
shape.append(ArcFactory.curve(previous_point, slope, point), PlanetariaShape.AppendMode.OverwriteWithEphemeral);
}
}
/// <summary>
/// Inspector/Constructor - Creates a copy of the shape then sets closed=true
/// </summary>
/// <returns>A closed shape mirroring all properties of original but with closed=true.</returns>
public void close(optional <Vector3> slope = new optional <Vector3>(), AppendMode permanence = AppendMode.OverwriteWithPermanent)
{
if (permanence == AppendMode.OverwriteWithEphemeral ||
permanence == AppendMode.OverwriteWithPermanent)
{
serialized_arc_list.RemoveRange(serialized_arc_list.Count - ephemeral_arcs, ephemeral_arcs);
ephemeral_arcs = 0;
}
// Add last edge! (if not already closed and Dot of last/first point is != 1)
if (!closed())
{
Arc first_arc = serialized_arc_list[0];
Arc last_arc = serialized_arc_list[serialized_arc_list.Count - 1];
if (!slope.exists)
{
slope = first_arc.begin();
}
append(ArcFactory.curve(last_arc.end(), slope.data, first_arc.begin()), permanence);
}
initialize();
// TODO: if field, make this a convex_hull() // TODO: add convex property
}
private static Vector3 prime_meridian_latitude(float latitude)
{
Arc prime_meridian = ArcFactory.curve(Vector3.back, Vector3.down, Vector3.back); // same as equator_longitude comment
return(prime_meridian.position(latitude));
}
private static Vector3 equator_longitude(float longitude)
{
Arc equator = ArcFactory.curve(Vector3.back, Vector3.left, Vector3.back); // The center of the arc is between begin and endpoint hence Vector3.back (not Vector3.forward) and Vector3.left (not Vector3.right)
return(equator.position(longitude));
}
/// <summary>
/// Inspector (Cache Mutator) - Updates the cache so that spherical rectangle calculations avoid recomputing old values.
/// </summary>
/// <param name="canvas">A Rect (measuring radians) representing the start and stop angles relative to Quaternion.identity. X/Y Range: (-2PI, +2PI).</param>
public static void cache_spherical_rectangle(Rect canvas)
{
if (cached_canvas != canvas)
{
Vector3 lower_left = intersection(canvas.xMin, canvas.yMin);
Vector3 lower_center = intersection(canvas.center.x, canvas.yMin);
Vector3 lower_right = intersection(canvas.xMax, canvas.yMin);
Vector3 middle_left = intersection(canvas.xMin, canvas.center.y);
Vector3 middle_center = intersection(canvas.center.x, canvas.center.y);
Vector3 middle_right = intersection(canvas.xMax, canvas.center.y);
Vector3 upper_left = intersection(canvas.xMin, canvas.yMax);
Vector3 upper_center = intersection(canvas.center.x, canvas.yMax);
Vector3 upper_right = intersection(canvas.xMax, canvas.yMax);
Arc biangle_segment1 = ArcFactory.curve(upper_center, upper_right, -upper_center);
Arc biangle_segment2 = ArcFactory.curve(lower_center, lower_right, -lower_center);
cached_left_biangle_focus = PlanetariaIntersection.arc_arc_intersection(biangle_segment1, biangle_segment2, 0).data;
cached_left_positive_partition = Bearing.attractor(cached_left_biangle_focus, middle_left); // used for a dot product to determine if the angle applied for UV is +/-
if (Vector3.Dot(cached_left_positive_partition, middle_center) >= 0)
{
cached_left_start_angle = Vector3.Angle(cached_left_biangle_focus, middle_center) * Mathf.Deg2Rad;
cached_left_end_angle = Vector3.Angle(cached_left_biangle_focus, middle_left) * Mathf.Deg2Rad;
}
else
{
cached_left_start_angle = Vector3.Angle(-cached_left_biangle_focus, middle_center) * Mathf.Deg2Rad + Mathf.PI;
cached_left_end_angle = Vector3.Angle(-cached_left_biangle_focus, middle_left) * Mathf.Deg2Rad + Mathf.PI;
}
biangle_segment1 = ArcFactory.curve(upper_center, upper_left, -upper_center);
biangle_segment2 = ArcFactory.curve(lower_center, lower_left, -lower_center);
cached_right_biangle_focus = PlanetariaIntersection.arc_arc_intersection(biangle_segment1, biangle_segment2, 0).data;
cached_right_positive_partition = Bearing.attractor(cached_right_biangle_focus, middle_right); // used for a dot product to determine if the angle applied for UV is +/-
if (Vector3.Dot(cached_right_positive_partition, middle_center) >= 0)
{
cached_right_start_angle = Vector3.Angle(cached_right_biangle_focus, middle_center) * Mathf.Deg2Rad;
cached_right_end_angle = Vector3.Angle(cached_right_biangle_focus, middle_right) * Mathf.Deg2Rad;
}
else
{
cached_right_start_angle = Vector3.Angle(-cached_right_biangle_focus, middle_center) * Mathf.Deg2Rad + Mathf.PI;
cached_right_end_angle = Vector3.Angle(-cached_right_biangle_focus, middle_right) * Mathf.Deg2Rad + Mathf.PI;
}
biangle_segment1 = ArcFactory.curve(middle_left, upper_left, -middle_left);
biangle_segment2 = ArcFactory.curve(middle_right, upper_right, -middle_right);
cached_lower_biangle_focus = PlanetariaIntersection.arc_arc_intersection(biangle_segment1, biangle_segment2, 0).data;
cached_lower_positive_partition = Bearing.attractor(cached_lower_biangle_focus, lower_center); // used for a dot product to determine if the angle applied for UV is +/-
if (Vector3.Dot(cached_lower_positive_partition, middle_center) >= 0)
{
cached_lower_start_angle = Vector3.Angle(cached_lower_biangle_focus, middle_center) * Mathf.Deg2Rad;
cached_lower_end_angle = Vector3.Angle(cached_lower_biangle_focus, lower_center) * Mathf.Deg2Rad;
}
else
{
cached_lower_start_angle = Vector3.Angle(-cached_lower_biangle_focus, middle_center) * Mathf.Deg2Rad + Mathf.PI;
cached_lower_end_angle = Vector3.Angle(-cached_lower_biangle_focus, lower_center) * Mathf.Deg2Rad + Mathf.PI;
}
biangle_segment1 = ArcFactory.curve(middle_left, lower_left, -middle_left);
biangle_segment2 = ArcFactory.curve(middle_right, lower_right, -middle_right);
cached_upper_biangle_focus = PlanetariaIntersection.arc_arc_intersection(biangle_segment1, biangle_segment2, 0).data;
cached_upper_positive_partition = Bearing.attractor(cached_upper_biangle_focus, upper_center); // used for a dot product to determine if the angle applied for UV is +/-
if (Vector3.Dot(cached_upper_positive_partition, middle_center) >= 0)
{
cached_upper_start_angle = Vector3.Angle(cached_upper_biangle_focus, middle_center) * Mathf.Deg2Rad;
cached_upper_end_angle = Vector3.Angle(cached_upper_biangle_focus, upper_center) * Mathf.Deg2Rad;
}
else
{
cached_upper_start_angle = Vector3.Angle(-cached_upper_biangle_focus, middle_center) * Mathf.Deg2Rad + Mathf.PI;
cached_upper_end_angle = Vector3.Angle(-cached_upper_biangle_focus, upper_center) * Mathf.Deg2Rad + Mathf.PI;
}
cached_north_hemisphere = Bearing.attractor(middle_center, upper_center);
cached_east_hemisphere = Bearing.attractor(middle_center, middle_right);
cached_canvas = canvas;
}
}