/// <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); }
/// <summary> /// Mutator - find all intersections along x=0 or z=0 arcs in southern hemisphere. /// </summary> /// <param name="block">The block (set of arcs) to be inspected.</param> private static void find_discontinuities(PlanetariaCollider collider) { foreach (Arc arc in collider.shape.arcs) { for (int dimension = 0; dimension < 2; ++dimension) // Intersect already gets quadrants 3-4 by proxy { float angle = (Mathf.PI / 2) * dimension; Vector3 begin = new Vector3(Mathf.Cos(angle), 0, Mathf.Sin(angle)); Vector3 end = Vector3.down; Vector3[] intersections = PlanetariaIntersection.arc_path_intersections(arc, begin, end, 0); add_intersections(arc, intersections); } } }
public bool is_self_intersecting() { List <Arc> edges = generate_edges(); for (int left = 0; left < edges.Count; ++left) { for (int right = left + 1; right < edges.Count; ++right) { optional <Vector3> intersection = PlanetariaIntersection.arc_arc_intersection(edges[left], edges[right], 0); if (intersection.exists) { return(true); } } } return(false); }
private void initialize() { arc_angle = arc_visitor.arc.angle(); float floor_length = arc_visitor.arc.length(); // edge case float ceiling_length = arc_visitor.arc.length(2 * offset); // corner case arc_length = Mathf.Max(floor_length, ceiling_length); // use longer distance to make movement feel consistent left_angle_boundary = -arc_angle / 2; if (concave(arc_visitor[-1], offset)) // set left boundary { optional <Vector3> intersection = PlanetariaIntersection.arc_arc_intersection(arc_visitor[0], arc_visitor[-2], offset); left_angle_boundary = arc_visitor.arc.position_to_angle(intersection.data); } right_angle_boundary = +arc_angle / 2; if (concave(arc_visitor[+1], offset)) // set right boundary { optional <Vector3> intersection = PlanetariaIntersection.arc_arc_intersection(arc_visitor[0], arc_visitor[+2], offset); right_angle_boundary = arc_visitor.arc.position_to_angle(intersection.data); } }
public static optional <BlockCollision> block_collision(CollisionObserver observer, Arc arc, PlanetariaCollider collider, PlanetariaTransform transformation, PlanetariaRigidbody rigidbody) { optional <ArcVisitor> arc_visitor = collider.shape.arc_visitor(arc); if (!arc_visitor.exists) { Debug.LogError("This should never happen"); return(new optional <BlockCollision>()); } Quaternion block_to_world = collider.gameObject.internal_game_object.transform.rotation; Quaternion world_to_block = Quaternion.Inverse(block_to_world); Vector3 last_position = world_to_block * rigidbody.get_previous_position(); Vector3 current_position = world_to_block * rigidbody.get_position(); float extrusion = transformation.scale / 2; optional <Vector3> intersection_point = PlanetariaIntersection.arc_path_intersection(arc, last_position, current_position, extrusion); if (!intersection_point.exists) // theoretically only happens with moving objects for discrete collision checks { // these functions are general inverses of one another, but also serve to constrain/normalize the position to the arc path. float intersection_angle = arc.position_to_angle(current_position); if (Mathf.Abs(intersection_angle) <= arc.angle() / 2) // if the intersection is valid { intersection_point = arc.position(intersection_angle); // set the collision to the extruded collision point } } if (!intersection_point.exists) { Debug.LogError("Research why this happened."); return(new optional <BlockCollision>()); } BlockCollision result = new BlockCollision(); float angle = arc.position_to_angle(intersection_point.data); result.geometry_visitor = ShapeVisitor.geometry_visitor(arc_visitor.data, angle, extrusion, collider.gameObject.internal_game_object.transform); intersection_point.data = block_to_world * intersection_point.data; result.distance = Vector3.Angle(intersection_point.data, rigidbody.get_previous_position()) * Mathf.Deg2Rad; result.overshoot = Vector3.Angle(intersection_point.data, rigidbody.get_position()) * Mathf.Deg2Rad; result.observer = observer; result.self = observer.collider(); result.other = collider; PlanetariaPhysicMaterial self = result.self.material; PlanetariaPhysicMaterial other = result.other.material; result.elasticity = PlanetariaPhysics.blend( self.elasticity, self.elasticity_combine, other.elasticity, other.elasticity_combine); result.friction = PlanetariaPhysics.blend( self.friction, self.friction_combine, other.friction, other.friction_combine); result.magnetism = -(self.magnetism - other.magnetism * self.induced_magnetism_multiplier) * (other.magnetism - self.magnetism * other.induced_magnetism_multiplier); return(result); }
/// <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; } }