private static float MaxErrorLocation(ArcOfSphere arc, float begin, float end)
{
Vector2 L1 = SpaceConverter.SphereToUV(arc.Evaluate(begin));
Vector2 L2 = SpaceConverter.SphereToUV(arc.Evaluate(end));
// 2) use binary / bisection search to find the point of maximal error
while (end - begin > delta)
{
float midpoint = (begin + end) / 2;
float error_left = Point_Line_Distance(L1, L2, SpaceConverter.SphereToUV(arc.Evaluate(midpoint - delta)));
float error_right = Point_Line_Distance(L1, L2, SpaceConverter.SphereToUV(arc.Evaluate(midpoint + delta)));
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 static ConcaveCorner Spawn(ArcOfSphere previous_edge, ArcOfSphere next_edge)
{
GameObject prefab = (GameObject)Resources.Load("ConcaveCornerPrefab");
#if UNITY_EDITOR
GameObject obj = PrefabUtility.InstantiatePrefab(prefab) as GameObject;
#else
GameObject obj = Instantiate(prefab) as GameObject;
#endif
#if UNITY_EDITOR
Undo.RegisterCreatedObjectUndo(obj, "Created concave corner");
#endif
obj.name = "Concave corner";
ConcaveCorner result = obj.GetComponent <ConcaveCorner>();
result.Initialize(previous_edge, next_edge);
#if UNITY_EDITOR
result.Save();
result.LinkBlock(previous_edge);
#endif
return(result);
}
public void GroundedUpdate(CharacterMotor self)
{
if (self.input.sqrMagnitude > 1)
{
self.input.Normalize();
}
Vector3 input3D = new Vector3(self.input.x, self.input.y, 0f); //FIXME: JANK
if (input3D.sqrMagnitude > 1)
{
input3D.Normalize();
}
Quaternion rotation = Quaternion.LookRotation(self.current_position, self.arc.EvaluateNormal(self.angle, self.radius));
float left_product = Vector3.Dot(rotation * input3D, self.left);
float right_product = Vector3.Dot(rotation * input3D, self.right);
float product = -Mathf.Abs(left_product);
if (right_product > left_product)
{
product = +Mathf.Abs(right_product);
}
if (right_product < 0 && left_product < 0)
{
product = 0;
}
self.angle += product / self.height / 64; //FIXME: slight math error here-ish
self.current_position = ArcOfSphere.Evaluate(self.ground.data, self.radius);
self.transform.rotation = Quaternion.LookRotation(self.current_position, self.arc.EvaluateNormal(self.angle, self.radius));
}
public bool Traverse(ArcOfSphere path, Vector3 desiredPos) //I don't like these parameters, they can be fixed //I don't like that this is public, it should be private and exposed via a generic move option if possible
{
optional <float> interpolation_factor = path.CartesianToRadial(desiredPos);
if (interpolation_factor.exists)
{
ground = new GroundInfo();
ground.data.angle = interpolation_factor.data;
ground.data.arc = path;
ground.data.block = path.GetComponentInParent <Block>();
ground.data.height = path.LengthRadius(radius);
ground.data.begin = path.Begin(radius);
ground.data.end = path.End(radius);
current_position = ArcOfSphere.Evaluate(ground.data, radius);
}
else
{
Debug.Log("Critical Failure: Traverse's interpolation factor doesn't exist!");
}
return(interpolation_factor.exists);
}
//step 0: Character Controller adds the observed SphericalIsoscelesTriangle to a vector in OnTriggerEnter...
public void OnTriggerEnter(Collider col)
{
ArcOfSphere arc = col.gameObject.GetComponent <ArcOfSphere>();
if (arc && !colliders.Contains(arc))
{
colliders.Add(arc);
}
}
//step 0.5: Character Controller removes the observed SphericalIsoscelesTriangle from a vector in OnTriggerExit...
public void OnTriggerExit(Collider col) //FIXME: not deleting
{
ArcOfSphere arc = col.gameObject.GetComponent <ArcOfSphere>();
if (arc)
{
colliders.Remove(arc);
}
}
public QuadraticBezier(ArcOfSphere a, Vector2 b, Vector2 c, Vector2 e, float bt, float et)
{
begin_UV = b;
control_point = c;
end_UV = e;
arc = a;
begin = bt;
end = et;
}
public static Edge LinkRight(ArcOfSphere left, Vector3 position)
{
Vector3 right = left.Evaluate(left.End());
Edge obj = Edge.StartEdge(left.transform.parent.transform, right, position);
obj.Relink(left, left.next);
return(obj);
}
protected static Vector3 MaxGradient(ArcOfSphere arc, Vector3 desired)
{
Vector3 max_gradient = Vector3.zero;
float max_product = Mathf.NegativeInfinity;
/** if we don't calculate per quadrant, calculations for an arc with angle 2*PI become ambiguous because left == right
*/
float quadrants = Mathf.Ceil(arc.End() / (Mathf.PI / 2f)); //maximum of 4, always integral, float for casting "left" and "right"
for (float quadrant = 0; quadrant < quadrants; ++quadrant)
{
float left = arc.End() * (quadrant / quadrants); //get beginning of quadrant i.e. 0.00,0.25,0.50,0.75
float right = arc.End() * ((quadrant + 1) / quadrants); //get end of quadrant i.e. 0.25,0.50,0.75,1.00
float left_product = Vector3.Dot(arc.Evaluate(left), desired); //find the correlation factor between left and the desired direction
float right_product = Vector3.Dot(arc.Evaluate(right), desired);
/** this is basically a binary search
*
* 1) take the left and right vectors and compute their dot products with the desired direction.
* 2) take the lesser dot product and ignore that half of the remaining arc
*/
for (int iteration = 0; iteration < 8 * sizeof(float); ++iteration) //because we are dealing with floats, more precision could help (or hurt?)
{
float midpoint = (left + right) / 2;
if (left_product < right_product) //is the right vector closer to the desired direction?
{
left = midpoint; //throw out the left half if the right vector is closer
left_product = Vector3.Dot(arc.Evaluate(left), desired);
}
else
{
right = midpoint; //throw out the right half if the left vector is closer
right_product = Vector3.Dot(arc.Evaluate(right), desired);
}
}
/** figure out if this quadrant contains a larger gradient
*/
if (max_product < right_product)
{
max_gradient = arc.Evaluate(right);
max_product = right_product;
}
if (max_product < left_product)
{
max_gradient = arc.Evaluate(left);
max_product = left_product;
}
}
return(max_gradient);
}
private static void UpdateSigns(ArcOfSphere arc, ref int[,] data, float location, float delta)
{
//assert data's size is [2, 3]
for (int dimension = 0; dimension < 3; ++dimension)
{
data[0, dimension] = System.Math.Sign(arc.Evaluate(location)[dimension]);
}
for (int dimension = 0; dimension < 3; ++dimension)
{
data[1, dimension] = System.Math.Sign(arc.Evaluate(location + delta)[dimension] - arc.Evaluate(location)[dimension]) * System.Math.Sign(delta);
}
}
public static void AddLine(ArcOfSphere edge, float begin, float end)
{
Vector2 begin_UV = SpaceConverter.SphereToUV(edge.Evaluate(begin));
Vector2 end_UV = SpaceConverter.SphereToUV(edge.Evaluate(end));
if (Vector2.Distance(begin_UV, end_UV) > threshold)
{
Vector2 delta_begin_UV = SpaceConverter.SphereToUV(edge.Evaluate(begin + 64 * delta));
Vector2 delta_end_UV = SpaceConverter.SphereToUV(edge.Evaluate(end - 64 * delta));
Vector2 control_point = Intersection(begin_UV, delta_begin_UV, delta_end_UV, end_UV);
DebugUtility.Log("AddLine:", begin_UV, end_UV);
lines.Add(new QuadraticBezier(edge, begin_UV, control_point, end_UV, begin, end));
}
}
public ArcOfSphere Relink(ArcOfSphere left, ArcOfSphere right)
{
#if UNITY_EDITOR
this.Save();
left.Save();
right.Save();
#endif
this.next = right;
this.prev = left;
left.next = this;
right.prev = this;
return(this);
}
public void Activate()
{
SphereCollider region = GetComponent <SphereCollider>();
Collider[] arc_objects = Physics.OverlapSphere(region.transform.position + region.center, region.transform.localScale.x * region.radius);
region.enabled = true;
foreach (Collider arc_object in arc_objects)
{
ArcOfSphere arc = arc_object.gameObject.GetComponent <ArcOfSphere>();
if (arc)
{
colliders.Add(arc);
}
}
}
public void Move(Vector2 input)
{
if (between_levels) //FEATURE: enable movement (grounded and aerial) in between_levels
{
connection.data.Move(Input.GetAxis("Vertical"), this);
}
else if (grounded) //FIXME: this entire block if it is JANK //spelling -_-'
{
if (input.sqrMagnitude > 1)
{
input.Normalize();
}
Transform camera_transform = GameObject.Find("MainCamera").transform; //FIXME: JANK
Vector3 input3D = new Vector3(input.x, input.y, 0f); //FIXME: JANK
if (input3D.sqrMagnitude > 1)
{
input3D.Normalize();
}
float left_product = Vector3.Dot(camera_transform.rotation * input3D, left);
float right_product = Vector3.Dot(camera_transform.rotation * input3D, right);
float product = -Mathf.Abs(left_product);
if (right_product > left_product)
{
product = +Mathf.Abs(right_product);
}
if (right_product < 0 && left_product < 0)
{
product = 0;
}
angle += product / height / 64; //FIXME: slight math error here-ish
current_position = ArcOfSphere.Evaluate(ground.data, radius);
transform.rotation = Quaternion.LookRotation(current_position, arc.EvaluateNormal(angle, radius));
}
else
{
SphereUtility.Accelerate(ref phi, ref theta, ref vertical_velocity, ref horizontal_velocity, 0.03f, -input.x / 10, Time.fixedDeltaTime);
current_position = SphereUtility.SphereToCartesian(new Vector2(phi, theta));
transform.rotation = Quaternion.LookRotation(current_position, North);
}
}
private static void Subdivide(ArcOfSphere arc, float begin, float end)
{
float midpoint = MaxErrorLocation(arc, begin, end);
Vector2 L1 = SpaceConverter.SphereToUV(arc.Evaluate(begin));
Vector2 L2 = SpaceConverter.SphereToUV(arc.Evaluate(end));
Vector2 P = SpaceConverter.SphereToUV(arc.Evaluate(midpoint));
if (Point_Line_Distance(L1, L2, P) > 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, midpoint);
Subdivide(arc, midpoint, end);
}
else
{
AddLine(arc, begin, end);
}
}
/** Create a AABB that perfectly contains a circular arc
*
* TODO: detailed description and math link
*
* TODO: Ex.
*
* @param collider the box collider that will be altered to contain the ArcOfSphere
*/
protected static void RecalculateAABB(ArcOfSphere arc)
{
float x_min = MaxGradient(arc, Vector3.left).x;
float x_max = MaxGradient(arc, Vector3.right).x;
float y_min = MaxGradient(arc, Vector3.down).y;
float y_max = MaxGradient(arc, Vector3.up).y;
float z_min = MaxGradient(arc, Vector3.back).z;
float z_max = MaxGradient(arc, Vector3.forward).z;
arc.transform.position = new Vector3((x_max + x_min) / 2,
(y_max + y_min) / 2,
(z_max + z_min) / 2);
BoxCollider collider = arc.GetComponent <BoxCollider>();
collider.size = new Vector3(x_max - x_min,
y_max - y_min,
z_max - z_min);
}
public override void Initialize(ArcOfSphere left, ArcOfSphere right)
{
#if UNITY_EDITOR
this.Save();
#endif
Vector3 path_center = right.Evaluate(right.Begin());
//Debug.DrawRay(path_center, Vector3.up, Color.yellow);
path_normal = right.Evaluate(right.Begin());
arc_left = left.EvaluateNormal(left.End());
arc_right = right.EvaluateNormal(right.Begin());
Initialize(path_center);
this.Relink(left, right);
}
public static void Append(GameObject shape)
{
lines = new List <QuadraticBezier>();
ArcOfSphere first_edge = shape.GetComponentInChildren <Edge>();
ArcOfSphere arc = first_edge;
do
{
float begin = arc.Begin();
float end = arc.End();
float range_begin = arc.Begin();
float range_end = arc.End();
float range_mid = arc.End() / 2;
int[,] xyz_signs_begin = new int[2, 3]; //positional, derivative; x, y, z
int[,] xyz_signs_end = new int[2, 3];
int[,] xyz_signs_range_begin = new int[2, 3]; //immediately before the first detected change in sign
int[,] xyz_signs_range_end = new int[2, 3]; //the first detected change in any sign
int[,] xyz_signs_range_mid = new int[2, 3]; //middle of begin and range_end
// get signs for beginning and end
UpdateSigns(arc, ref xyz_signs_begin, arc.Begin(), delta);
UpdateSigns(arc, ref xyz_signs_end, arc.End(), -delta);
// process new lines until the signs match
while (!SameSigns(ref xyz_signs_begin, ref xyz_signs_end))
{
xyz_signs_range_begin = xyz_signs_begin;
xyz_signs_range_end = xyz_signs_end;
// binary search and discard ranges with matching slope signs and position signs at ends; and then update the slope signs.
while (range_end - range_begin > delta)
{
range_mid = (range_begin + range_end) / 2; //guaranteed not to overflow since numbers are in range [0, 2pi]
UpdateSigns(arc, ref xyz_signs_range_mid, range_mid, delta);
if (SameSigns(ref xyz_signs_range_begin, ref xyz_signs_range_mid))
{
range_begin = range_mid;
//xyz_signs_begin = xyz_signs_range_mid; //not necessary, the signs are the same
}
else
{
range_end = range_mid;
xyz_signs_range_end = xyz_signs_range_mid;
}
}
// when you find a sign that switches, log the exact position of the switch with as much precision as possible
Subdivide(arc, begin, range_begin);
// when you find that position, you must then switch the x, y, z signs at the new beginning of the arc and the slope signs xyz at the beginning of the arc
begin = range_end;
xyz_signs_begin = xyz_signs_range_end;
}
// draw the last line
Subdivide(arc, begin, end);
arc = arc.next; // move to next arc
while (arc.GetType().IsSubclassOf(typeof(Corner))) // skip corners //XXX: Corner is abstract... for now
{
arc = arc.next;
}
} while (arc != first_edge);
ClampToEdges();
OverlapSharedEdges();
BuildShape();
}
public virtual void Initialize(ArcOfSphere left, ArcOfSphere right)
{
}
public void LinkBlock(ArcOfSphere other)
{
LinkBlock(other.gameObject.transform.parent);
}
