// Update is called once per frame
void Update()
{
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
Vector3 v2 = P2.transform.localPosition - P0.transform.localPosition;
float dot = Vector3.Dot(v1, v2);
float cosTheta = float.NaN;
float theta = float.NaN;
if (Mathf.Abs(dot) > float.Epsilon) // make sure dot is properly defined
{
cosTheta = dot / (v1.magnitude * v2.magnitude);
theta = Mathf.Acos(cosTheta) * Mathf.Rad2Deg;
}
Debug.Log("Dot result=" + dot + " cosTheta=" + cosTheta + " angle=" + theta);
#region For visualizing the vectors
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowV2.VectorFromTo(P0.transform.localPosition, P2.transform.localPosition);
ShowNV2.VectorAt = P1.transform.localPosition;
ShowNV2.Direction = -ShowV2.Direction;
ShowNV2.Magnitude = ShowV2.Magnitude;
Vector3 v1_v2 = v1 - v2;
ShowV1_V2.Direction = v1_v2;
ShowV1_V2.Magnitude = v1_v2.magnitude;
ShowV1_V2.VectorAt = P2.transform.localPosition;
ShowV1_V2_Pos.Direction = ShowV1_V2.Direction;
ShowV1_V2_Pos.Magnitude = ShowV1_V2.Magnitude;
ShowV1_V2_Pos.VectorAt = P0.transform.localPosition;
#endregion
}
// Update is called once per frame
void Update()
{
#region Visualization on/off: show or hide to avoid clutering
AxisFrame.ShowAxisFrame = DrawAxisFrame; // Draw or Hide Axis Frame
P1.SetActive(DrawPositionAsVector); // objects that suppor position as vector
P2.SetActive(DrawPositionAsVector);
Pd.SetActive(DrawPositionAsVector);
Pi.SetActive(DrawVectorAsPosition); // objects that support vector as positions
Pj.SetActive(DrawVectorAsPosition);
Pe.SetActive(DrawVectorAsPosition);
ShowVdAtP1.DrawVector = DrawPositionAsVector; // Display or hide the vectors
ShowVd.DrawVector = DrawPositionAsVector;
ShowVeAtPi.DrawVector = DrawVectorAsPosition;
ShowVe.DrawVector = DrawVectorAsPosition;
#endregion
#region Position Vector: Show Pd as a vector at P1
if (DrawPositionAsVector)
{
// Use position of Pd as position vector
Vector3 vectorVd = Pd.transform.localPosition;
// Step 1: take care of visualization
// for Vd
ShowVd.Direction = vectorVd;
ShowVd.Magnitude = vectorVd.magnitude;
// apply Vd at P1
ShowVdAtP1.VectorAt = P1.transform.localPosition; // Always draw at P1
ShowVdAtP1.Magnitude = vectorVd.magnitude; // get from vectorVd
ShowVdAtP1.Direction = vectorVd;
// Step 2: demonstrate P2 is indeed Vd away from P1
P2.transform.localPosition = P1.transform.localPosition + vectorVd;
}
#endregion
#region Vector from two points: Show Ve as the position Pe
if (DrawVectorAsPosition)
{
// Use from Pi to Pj as vector for Ve
Vector3 vectorVe = Pj.transform.localPosition - Pi.transform.localPosition;
// Step 1: Take care of visualization
// for Ve: from Pi to Pj
ShowVeAtPi.VectorFromTo(Pi.transform.localPosition, Pj.transform.localPosition);
// Show as Ve at the origin
ShowVe.Direction = vectorVe;
ShowVe.Magnitude = vectorVe.magnitude;
// Step 2: demonstrate Pe is indeed Ve away from the origin
Pe.transform.localPosition = vectorVe;
}
#endregion
}
// Update is called once per frame
void Update()
{
float distance = 0; // closest distance
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
float v1Len = v1.magnitude;
if (v1Len > float.Epsilon)
{
Vector3 vt = Pt.transform.localPosition - P0.transform.localPosition;
Vector3 v1n = (1f / v1Len) * v1; // <<-- what is going on here?
float d = Vector3.Dot(vt, v1n);
if (d < 0)
{
Pon.transform.localPosition = P0.transform.localPosition;
distance = vt.magnitude;
}
else if (d > v1Len)
{
Pon.transform.localPosition = P1.transform.localPosition;
distance = (Pt.transform.localPosition - P1.transform.localPosition).magnitude;
}
else
{
Pon.transform.localPosition = P0.transform.localPosition + d * v1n;
Vector3 von = Pon.transform.localPosition - Pt.transform.localPosition;
distance = von.magnitude;
}
float s = distance * kScaleFactor;
Pon.transform.localScale = new Vector3(s, s, s);
Debug.Log("v1Len=" + v1Len + " d=" + d + " Distance=" + distance);
}
#region For visualizing the lines
bool visible = v1Len > float.Epsilon;
ShowVc.DrawVector = visible;
ShowLine.DrawVector = visible;
ShowV1.DrawVector = visible;
if (v1Len > float.Epsilon)
{
Vector3 vt = Pt.transform.localPosition - P0.transform.localPosition;
Vector3 v1n = (1f / v1Len) * v1; // <<-- what am I doing here?
float d = Vector3.Dot(v1n, vt);
ShowLine.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowVc.VectorFromTo(Pt.transform.localPosition, Pon.transform.localPosition);
float after = 0.45f;
float before = 0.15f;
Vector3 pv0 = P0.transform.localPosition - before * v1;;
Vector3 pv1 = P1.transform.localPosition + after * v1;
ShowV1.VectorFromTo(pv0, pv1);
}
#endregion
}
// Update is called once per frame
void Update()
{
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
#region For visualizing the vectors
Vector3 pv0 = P0.transform.localPosition - 0.5f * v1;
Vector3 pv1 = P1.transform.localPosition + 0.5f * v1;
ShowV1.VectorFromTo(pv0, pv1);
Pa.transform.localPosition = P0.transform.localPosition - 0.18f * v1;
Pb.transform.localPosition = P0.transform.localPosition + 1.2f * v1;
ShowLine.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
#endregion
}
// Update is called once per frame
void Update()
{
aVector.DrawVector = ShowA;
sVector.DrawVector = ShowS;
cutVector.DrawVector = ShowC;
Vector3 d = Dst.transform.localPosition - Src.transform.localPosition;
aVector.Direction = d;
aVector.VectorAt = aPos.transform.localPosition;
aVector.Magnitude = size;
sVector.VectorAtDirLength(aVector.VectorAt + Vector3.right, d, aVector.Magnitude);
cutVector.VectorFromTo(Src.transform.localPosition, Dst.transform.localPosition);
}
// Update is called once per frame
void Update()
{
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
#region For visualizing the vectors
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
float r = 0.8f * v1.magnitude;
Vector3 p0 = P0.transform.localPosition;
float delta = 45;
for (int i = 0; i < ShowV2.Length; i++)
{
float d = (i + 1) * delta * Mathf.Deg2Rad;
float x = r * Mathf.Cos(d);
float y = r * Mathf.Sin(d);
Vector3 t = new Vector3(x, y, 0);
ShowV2[i].VectorFromTo(p0, t);
}
#endregion
}
// Update is called once per frame
void Update()
{
float cosTheta = float.NaN;
float theta = float.NaN;
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
Vector3 v2 = P2.transform.localPosition - P0.transform.localPosition;
float dot = Vector3.Dot(v1, v2);
if ((v1.magnitude > float.Epsilon) && (v2.magnitude > float.Epsilon))
{
cosTheta = dot / (v1.magnitude * v2.magnitude);
// Alternatively,
// costTheta = Vector3.Dot(v1.normalize, v2.normalize)
theta = Mathf.Acos(cosTheta) * Mathf.Rad2Deg;
}
Debug.Log("Dot result=" + dot + " cosTheta=" + cosTheta + " angle=" + theta);
#region For visualizing the vectors
ShowPlane.DrawPlane = DrawThePlane;
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowV2.VectorFromTo(P0.transform.localPosition, P2.transform.localPosition);
Vector3 dotP = Vector3.zero;
ShowPlane.DrawPlane &= cosTheta != float.NaN;
ShowDot.DrawVector = cosTheta != float.NaN;
if (cosTheta != float.NaN)
{
float r = 3f * Mathf.Abs(cosTheta);
dotP.x = r * cosTheta;
dotP.y = r * Mathf.Sin(theta * Mathf.Deg2Rad);
ShowDot.VectorFromTo(Vector3.zero, dotP);
if (Mathf.Abs(cosTheta) < (1f - float.Epsilon))
{
// The plane
Vector3 n = Vector3.Cross(v1, v2);
if (Vector3.Dot(n, Vector3.forward) > 0)
{
n = -n;
}
float s = Mathf.Max(v1.magnitude, v2.magnitude);
ShowPlane.XSize = ShowPlane.ZSize = s * 0.7f;
ShowPlane.PlaneNormal = n;
ShowPlane.Center = (P0.transform.localPosition + P1.transform.localPosition + P2.transform.localPosition) / 3f;
}
else
{
ShowPlane.DrawPlane = false;
}
}
if (dot > 0f)
{
ShowDot.VectorColor = PositiveColor;
}
else
{
ShowDot.VectorColor = NegativeColor;
}
#endregion
}
// Update is called once per frame
void Update()
{
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
Vector3 v2 = P2.transform.localPosition - P0.transform.localPosition;
if ((v1.magnitude > float.Epsilon) &&
(v2.magnitude > float.Epsilon))
// make sure v1 and v2 are not zero vectors
{
switch (ProjChoice)
{
case ProjectionChoice.V1OntoV2:
float v1LengthonV2 = Vector3.Dot(v1, v2.normalized);
Debug.Log("Projection Result: Length of V1 along V2 = " + v1LengthonV2);
break;
case ProjectionChoice.V2OntoV1:
float v2LengthonV1 = Vector3.Dot(v1.normalized, v2);
Debug.Log("Projection Result: Length of V2 along V1 = " + v2LengthonV1);
break;
default:
Debug.Log("Projection Result: no projection, dot=" + Vector3.Dot(v1, v2));
break;
}
}
#region For visualizing the vectors
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowV2.VectorFromTo(P0.transform.localPosition, P2.transform.localPosition);
ShowProjected.DrawVector = (v1.magnitude > float.Epsilon) && (v2.magnitude > float.Epsilon) && (ProjChoice != ProjectionChoice.ProjectionOff);
ShowProjectedAlone.DrawVector = ShowProjected.DrawVector;
ShowProjected.VectorColor = PositiveColor;
ShowProjectedAlone.VectorColor = PositiveColor;
float length = 0f;
if (ShowProjected.DrawVector)
{
if (ProjChoice == ProjectionChoice.V1OntoV2)
{
Vector3 nv = v2.normalized;
length = Vector3.Dot(v1, nv);
Vector3 pt = P0.transform.localPosition + length * nv;
ShowProjected.VectorFromTo(P0.transform.localPosition, pt);
Debug.DrawLine(P1.transform.localPosition, pt, Color.black);
}
else
{
Vector3 nv = v1.normalized;
length = Vector3.Dot(v2, nv);
Vector3 pt = P0.transform.localPosition + length * nv;
ShowProjected.VectorFromTo(P0.transform.localPosition, pt);
Debug.DrawLine(P2.transform.localPosition, pt, Color.black);
}
ShowProjectedAlone.VectorAt = P0.transform.localPosition - Vector3.right;
ShowProjectedAlone.Magnitude = ShowProjected.Magnitude;
if (length > 0)
{
ShowProjectedAlone.Direction = Vector3.up;
ShowProjectedAlone.VectorColor = Color.black;
ShowProjected.VectorColor = PositiveColor;
}
else
{
ShowProjectedAlone.Direction = -Vector3.up;
ShowProjectedAlone.VectorColor = Color.red;
ShowProjected.VectorColor = NegativeColor;
}
}
#endregion
}
// Update is called once per frame
void Update()
{
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
if (v1.magnitude > float.Epsilon)
{
Vector3 vt = Pt.transform.localPosition - P0.transform.localPosition;
Vector3 v1n = v1.normalized;
float d = Vector3.Dot(vt, v1n);
Pon.transform.localPosition = P0.transform.localPosition + d * v1.normalized;
if ((d >= 0) && (d <= v1.magnitude))
{
Debug.Log("V1.mag=" + v1.magnitude + " Projected Length=" + d + " ==> Inside!");
}
else
{
Debug.Log("V1.mag=" + v1.magnitude + " Projected Length=" + d + " ==> Outside!");
}
}
#region For visualizing the vectors
ShowLine.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
bool visible = v1.magnitude > float.Epsilon;
ShowV1.DrawVector = visible;
ShowPv.DrawVector = visible;
ShowPa.DrawVector = visible;
if (visible)
{
Vector3 v1n = v1.normalized;
Vector3 vt = Pt.transform.localPosition - P0.transform.localPosition;
float d = Vector3.Dot(vt, v1n);
if (d >= 0 && d <= v1.magnitude)
{
ShowLine.VectorColor = MyDrawObject.CollisionColor;
}
else
{
ShowLine.VectorColor = MyDrawObject.NoCollisionColor;
}
ShowPv.VectorFromTo(P0.transform.localPosition, Pt.transform.localPosition);
ShowPa.VectorFromTo(Pt.transform.localPosition, Pon.transform.localPosition);
float after = 0.45f;
float before = 0.15f;
Vector3 pv0 = P0.transform.localPosition - before * v1;;
Vector3 pv1 = P1.transform.localPosition + after * v1;
if (d > (((1f + after) * v1.magnitude) - 1f))
{
pv1 = Pon.transform.localPosition + v1n;
}
if (d < ((-before * v1.magnitude) + 1f))
{
pv0 = Pon.transform.localPosition - v1n;
}
ShowV1.VectorFromTo(pv0, pv1);
}
#endregion
}
// Update is called once per frame
void Update()
{
#region Identical to EX_6_2
// Computes V1 and V2
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
Vector3 v2 = P2.transform.localPosition - P0.transform.localPosition;
if ((v1.magnitude < float.Epsilon) || (v2.magnitude < float.Epsilon))
{
return;
}
// Plane equation parameters
Vector3 vn = Vector3.Cross(v1, v2);
vn.Normalize(); // keep this vector normalized
float D = Vector3.Dot(vn, P0.transform.localPosition);
// Showing the plane equation is consistent
Pn.transform.localPosition = D * vn;
Ds.transform.localScale = new Vector3(D * 2f, D * 2f, D * 2f); // sphere expects diameter
// Set up for displaying Pt and Pon
Pt.SetActive(ShowPointOnPlane);
Pon.SetActive(ShowPointOnPlane);
float t = 0;
bool almostParallel = false;
if (ShowPointOnPlane)
{
float d = Vector3.Dot(vn, Pt.transform.localPosition); // distance
almostParallel = (Mathf.Abs(d) < float.Epsilon);
Pon.SetActive(!almostParallel);
if (!almostParallel)
{
t = D / d;
Pon.transform.localPosition = t * Pt.transform.localPosition;
}
}
#endregion
float l1 = v1.magnitude;
float l2 = v2.magnitude;
Vector3 v2p = l2 * Vector3.Cross(vn, v1).normalized;
P2p.transform.localPosition = P0.transform.localPosition + v2p;
bool inside = false;
if (!almostParallel)
{
Vector3 von = Pon.transform.localPosition - P0.transform.localPosition;
float d1 = Vector3.Dot(von, v1.normalized);
float d2 = Vector3.Dot(von, v2p.normalized);
inside = ((d1 >= 0) && (d1 <= l1)) && ((d2 >= 0) && (d2 <= l2));
if (inside)
{
Debug.Log("Inside: Pon is inside of the region defined by V1 and V2");
}
else
{
Debug.Log("Outside: Pon is outside of the region defined by V1 and V2");
}
}
#region For visualizing the vectors
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowV2.VectorFromTo(P0.transform.localPosition, P2.transform.localPosition);
ShowV3.VectorFromTo(P0.transform.localPosition, P2p.transform.localPosition);
ShowVn.VectorAt = P0.transform.localPosition;
ShowVn.Direction = vn;
ShowVn.Magnitude = 2f;
ShowNormal.VectorAt = Vector3.zero;
ShowNormal.Magnitude = Mathf.Abs(D) + 2f;
ShowNormal.Direction = vn;
ShowPlane.PlaneNormal = -vn;
Vector3 at = P0.transform.localPosition + P1.transform.localPosition + P2.transform.localPosition + Pn.transform.localPosition;
int c = 4;
float scale = 1.0f;
ShowPtLine.DrawVector = ShowPointOnPlane;
float da = v1.magnitude * scale;
float db = v2.magnitude * scale;
float du = Mathf.Max(da, db);
if (ShowPointOnPlane && (!almostParallel))
{
Pon.GetComponent <Renderer>().material.color = Color.white;
float don = (Pon.transform.localPosition - P0.transform.localPosition).magnitude * scale;
at += Pon.transform.localPosition;
c++;
du = Mathf.Max(du, don);
// Now the line
ShowPtLine.VectorColor = Color.black;
if (Vector3.Dot(Pon.transform.localPosition, Pt.transform.localPosition) < 0)
{
ShowPtLine.VectorColor = Color.red;
ShowPtLine.VectorFromTo(Pt.transform.localPosition, Pon.transform.localPosition);
}
else
{
if (Pon.transform.localPosition.magnitude > Pt.transform.localPosition.magnitude)
{
ShowPtLine.VectorFromTo(Vector3.zero, Pon.transform.localPosition);
}
else
{
ShowPtLine.VectorFromTo(Vector3.zero, Pt.transform.localPosition);
}
}
if (!inside)
{
Pon.GetComponent <Renderer>().material.color = Color.red;
}
}
if (du < 0.5f)
{
du = 0.5f;
}
ShowPlane.XSize = ShowPlane.ZSize = du;
ShowPlane.Center = at / c;
#endregion
}
// Update is called once per frame
void Update()
{
// Computes V1 and V2
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
Vector3 v2 = P2.transform.localPosition - P0.transform.localPosition;
if ((v1.magnitude < float.Epsilon) || (v2.magnitude < float.Epsilon))
{
return;
}
// Plane equation parameters
Vector3 vn = Vector3.Cross(v1, v2);
vn.Normalize(); // keep this vector normalized
float D = Vector3.Dot(vn, P0.transform.localPosition);
// Showing the plane equation is consistent
Pn.transform.localPosition = D * vn;
Ds.transform.localScale = new Vector3(D * 2f, D * 2f, D * 2f); // sphere expects diameter
// Set up for displaying Pt and Pon
Pt.SetActive(ShowPointOnPlane);
Pon.SetActive(ShowPointOnPlane);
float t = 0;
bool almostParallel = false;
if (ShowPointOnPlane)
{
float d = Vector3.Dot(vn, Pt.transform.localPosition); // distance
almostParallel = (Mathf.Abs(d) < float.Epsilon);
Pon.SetActive(!almostParallel);
if (!almostParallel)
{
t = D / d;
Pon.transform.localPosition = t * Pt.transform.localPosition;
}
}
#region For visualizing the vectors
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowV2.VectorFromTo(P0.transform.localPosition, P2.transform.localPosition);
ShowVn.VectorAt = P0.transform.localPosition;
ShowVn.Direction = vn;
ShowVn.Magnitude = 2f;
ShowNormal.VectorAt = Vector3.zero;
ShowNormal.Magnitude = Mathf.Abs(D) + 2f;
ShowNormal.Direction = vn;
ShowPlane.PlaneNormal = -vn;
Vector3 at = P0.transform.localPosition + P1.transform.localPosition + P2.transform.localPosition + Pn.transform.localPosition;
int c = 4;
float scale = 1.0f;
ShowPtLine.DrawVector = ShowPointOnPlane;
float d1 = v1.magnitude * scale;
float d2 = v2.magnitude * scale;
float du = Mathf.Max(d1, d2);
if (ShowPointOnPlane && (!almostParallel))
{
float don = (Pon.transform.localPosition - P0.transform.localPosition).magnitude * scale;
at += Pon.transform.localPosition;
c++;
du = Mathf.Max(du, don);
// Now the line
ShowPtLine.VectorColor = Color.black;
if (Vector3.Dot(Pon.transform.localPosition, Pt.transform.localPosition) < 0)
{
ShowPtLine.VectorColor = Color.red;
ShowPtLine.VectorFromTo(Pt.transform.localPosition, Pon.transform.localPosition);
}
else
{
if (Pon.transform.localPosition.magnitude > Pt.transform.localPosition.magnitude)
{
ShowPtLine.VectorFromTo(Vector3.zero, Pon.transform.localPosition);
}
else
{
ShowPtLine.VectorFromTo(Vector3.zero, Pt.transform.localPosition);
}
}
}
if (du < 0.5f)
{
du = 0.5f;
}
ShowPlane.XSize = ShowPlane.ZSize = du;
ShowPlane.Center = at / c;
#endregion
}
// Update is called once per frame
void Update()
{
Vector3 v1 = P1.transform.localPosition - P0.transform.localPosition;
Vector3 v2 = P2.transform.localPosition - P0.transform.localPosition;
Vector3 v1xv2 = Vector3.Cross(v1, v2);
Vector3 v2xv1 = Vector3.Cross(v2, v1);
float d = Vector3.Dot(v1.normalized, v2.normalized);
bool notParallel = (Mathf.Abs(d) < (1.0f - float.Epsilon));
if (notParallel)
{
float theta = Mathf.Acos(d) * Mathf.Rad2Deg;
float cd = Vector3.Dot(v1xv2.normalized, v2xv1.normalized);
float dv1 = Vector3.Dot(v1xv2, v1);
float dv2 = Vector3.Dot(v1xv2, v2);
Debug.Log(" theta=" + theta + " v1xv2=" + v1xv2 + " v2xv1=" + v2xv1 + " v1xv2-dot-v2xv1=" + cd + " Dot with v1/v2=" + dv1 + " " + dv2);
}
else
{
Debug.Log("Two vectors are parallel, cross product is a zero vector");
}
#region For visualizing the vectors
ShowPlane.DrawPlane = DrawThePlane;
ShowV1xV2.DrawVector = DrawV1xV2;
ShowV2xV1.DrawVector = DrawV2xV1;
ShowV1.VectorFromTo(P0.transform.localPosition, P1.transform.localPosition);
ShowV2.VectorFromTo(P0.transform.localPosition, P2.transform.localPosition);
ShowPlane.DrawPlane &= notParallel;
ShowV1xV2.DrawVector &= notParallel;
ShowV2xV1.DrawVector &= notParallel;
if (notParallel)
{
ShowV1xV2.VectorAt = P0.transform.localPosition;
ShowV1xV2.Magnitude = v1xv2.magnitude * Factor;
ShowV1xV2.Direction = v1xv2;
ShowV2xV1.VectorAt = P0.transform.localPosition;
ShowV2xV1.Magnitude = v2xv1.magnitude * Factor;
ShowV2xV1.Direction = v2xv1;
// The plane
Vector3 n = Vector3.Cross(v1, v2);
if (Vector3.Dot(n, Vector3.forward) > 0)
{
n = -n;
}
float s = Mathf.Max(v1.magnitude, v2.magnitude);
ShowPlane.XSize = ShowPlane.ZSize = s;
ShowPlane.PlaneNormal = n;
ShowPlane.Center = (P0.transform.localPosition + P1.transform.localPosition + P2.transform.localPosition) / 3f;
}
#endregion
}
// Update is called once per frame
void Update()
{
#region Step 0: Initial error checking
Debug.Assert((Pc.transform.localPosition - Pb.transform.localPosition).magnitude > float.Epsilon);
Debug.Assert(Vn.magnitude > float.Epsilon);
Debug.Assert(Aspeed > float.Epsilon);
Debug.Assert(Tr > float.Epsilon);
// recoveries from the errors
if ((Pc.transform.localPosition - Pb.transform.localPosition).magnitude < float.Epsilon)
{
Pc.transform.localPosition = Pb.transform.localPosition - Vector3.forward;
}
if (Vn.magnitude < float.Epsilon)
{
Vn = Vector3.forward;
}
if (Aspeed < float.Epsilon)
{
Aspeed = 0.01f;
}
if (Tr < float.Epsilon)
{
Tr = 0.01f;
}
#endregion
#region Step 1: The Aiming System
Vector3 aDir = (Pc.transform.localPosition - Pb.transform.localPosition);
aDir.Normalize(); // assuming the two are not located at the same point
Pc.transform.localPosition = Pb.transform.localPosition + Aspeed * aDir;
if (!MoveAgent)
{ // controls only when agent is not moving
Pa.transform.localPosition = Pb.transform.localPosition + 2 * Aspeed * aDir;
Adir = aDir;
}
#endregion
#region Step 2: The Agent
if (MoveAgent)
{
Pa.transform.localPosition += Aspeed * Time.deltaTime * Adir;
AgentSinceTime += Time.deltaTime;
if (AgentSinceTime > AgentSentInterval)
{ // Time to re-send the agent from base
Pa.transform.localPosition = Pc.transform.localPosition;
Adir = aDir;
AgentSinceTime = 0f;
}
}
if (ShowVelocity && ShowDebugLines)
{
Debug.DrawLine(Pa.transform.localPosition, Pa.transform.localPosition + 20f * Adir, Color.red);
}
#endregion
#region Step 3: The Plane and infront/parellel checks
// Plane equation
Vn.Normalize();
Pn.transform.localPosition = D * Vn;
// agent position checks
float paDotVn = Vector3.Dot(Pa.transform.localPosition, Vn);
bool infrontOfPlane = (paDotVn > D);
// Agent motion direction checks
float aDirDotVn = Vector3.Dot(Adir, Vn);
bool isApproaching = (aDirDotVn < 0f);
bool notParallel = (Mathf.Abs(aDirDotVn) > float.Epsilon);
#endregion
#region Step 4: The Shadow
Ps.SetActive(CastShadow && infrontOfPlane);
if (CastShadow && infrontOfPlane)
{
float h = Vector3.Dot(Pa.transform.localPosition, Vn);
Ps.transform.localPosition = Pa.transform.localPosition - (h - D) * Vn;
if (ShowDebugLines)
{
Debug.DrawLine(Pa.transform.localPosition, Ps.transform.localPosition, Color.black);
}
}
#endregion
#region Step 5: The Reflection
Pon.SetActive(DoReflection && notParallel && infrontOfPlane && isApproaching);
Pr.SetActive(DoReflection && notParallel && infrontOfPlane && isApproaching);
Vector3 vr = Vector3.up; // Reflection vector
bool vrIsValid = false;
if (DoReflection && notParallel && isApproaching)
{
if (infrontOfPlane)
{
float d = (D - Vector3.Dot(Pa.transform.localPosition, Vn)) / aDirDotVn;
Pon.transform.localPosition = Pa.transform.localPosition + d * Adir;
Vector3 von = Pa.transform.localPosition - Pon.transform.localPosition; // von is simply -d*Adir
Vector3 m = (Vector3.Dot(von, Vn) * Vn) - von;
vr = 2 * m + von;
Pr.transform.localPosition = Pon.transform.localPosition + vr;
vrIsValid = true;
if (ShowDebugLines)
{
Debug.DrawLine(Pa.transform.localPosition, Pon.transform.localPosition, Color.red);
Debug.DrawLine(Pon.transform.localPosition, Pr.transform.localPosition, Color.red);
}
// if (von.magnitude < float.Epsilon) What will happen if you do this?
if (von.magnitude < 0.1f)
{
// collision!
Adir = vr.normalized;
}
}
else
{
Debug.Log("Potential problem!: high speed Agent, missing the plane collision?");
// What can you do?
}
}
#endregion
#region Step 6: The collision with treasure
Pt.SetActive(DoReflection && CollideTreasure);
Pt.transform.localScale = new Vector3(2 * Tr, 2 * Tr, 2 * Tr); // this is the diameter
Pt.GetComponent <Renderer>().material.color = MyDrawObject.NoCollisionColor;
if (DoReflection && CollideTreasure && vrIsValid)
{
Vector3 vt = Pt.transform.localPosition - Pon.transform.localPosition;
float dt = Vector3.Dot(vt, vr.normalized);
if ((dt >= 0) && (dt <= vr.magnitude))
{
Vector3 pdt = Pon.transform.localPosition + dt * vr.normalized;
if ((pdt - Pt.transform.localPosition).magnitude <= Tr)
{
Pt.GetComponent <Renderer>().material.color = MyDrawObject.CollisionColor;
}
}
}
#endregion
#region For visualation
AxisFrame.ShowAxisFrame = ShowAxisFrame;
if (ShowAxisFrame && ShowDebugLines)
{
Debug.DrawLine(Vector3.zero, Pn.transform.localPosition, Color.white);
}
// Aiming
ShowAim.VectorFromTo(Pb.transform.localPosition, Pc.transform.localPosition);
// Refleciton plane
ShowVrN.VectorAt = Pn.transform.localPosition;
ShowVrN.Magnitude = 2.0f;
ShowVrN.Direction = Vn;
ShowReflectionPlane.Center = Pn.transform.localPosition;
ShowReflectionPlane.PlaneNormal = Vn;
/*
* Do not adjust the plane size, it is confusing.
* const float S = 3f;
* float s = S;
* if (CastShadow || DoReflection)
* {
* if (CastShadow) {
* s = (Ps.transform.localPosition - Pn.transform.localPosition).magnitude * 0.3f;
* // ShowProj.VectorFromTo(Pa.transform.localPosition, Ps.transform.localPosition);
* }
* if (DoReflection)
* {
* float t = (Pon.transform.localPosition - Pn.transform.localPosition).magnitude * 0.3f;
* if (t > s)
* s *= 1.02f;
* else if (t < s)
* s *= 0.98f;
* // ShowToPn.VectorFromTo(Pa.transform.localPosition, Pon.transform.localPosition);
* // ShowFromPn.VectorFromTo(Pon.transform.localPosition, Pr.transform.localPosition);
* }
* }
* ShowReflectionPlane.XSize = ShowReflectionPlane.ZSize = s;
*/
#endregion
}