public Obb2d(vector center, vector extents, vector ax, vector ay)
{
Center = center;
Extents = extents;
Ax = ax;
Ay = ay;
}
public Obb2d(Obb2f v)
{
Center = new vector(v.Center);
Extents = new vector(v.Extents);
Ax = new vector(v.Ax);
Ay = new vector(v.Ay);
}
public Obb2d(aabb aabb)
{
Center = aabb.Center;
Extents = aabb.Extents;
Ax = vector.AxisX;
Ay = vector.AxisY;
}
/// <summary>
/// ３次ベジェ曲線での補間を微分する
/// </summary>
/// <param name="t">パラメータ</param>
/// <param name="p0">コントロールポイント０</param>
/// <param name="p1">コントロールポイント１</param>
/// <param name="p2">コントロールポイント２</param>
/// <param name="p3">コントロールポイント３</param>
/// <returns>微分結果のベクトル</returns>
public static vector DiffInterpolate3(element t, vector p0, vector p1, vector p2, vector p3)
{
var t2 = t * t;
var ti = 1 - t;
var ti2 = ti * ti;
return(p0 * (-3 * ti2) + p1 * (9 * t2 - 12 * t + 3) + p2 * (-9 * t2 + 6 * t) + p3 * (3 * t2));
}
/// <summary>
/// ３次ベジェ曲線で補間する
/// </summary>
/// <param name="t">パラメータ</param>
/// <param name="p0">コントロールポイント０</param>
/// <param name="p1">コントロールポイント１</param>
/// <param name="p2">コントロールポイント２</param>
/// <param name="p3">コントロールポイント３</param>
/// <returns>補間された座標</returns>
public static vector Interpolate3(element t, vector p0, vector p1, vector p2, vector p3)
{
var t2 = t * t;
var t3 = t2 * t;
var ti = 1 - t;
var ti2 = ti * ti;
var ti3 = ti2 * ti;
return(p0 * ti3 + p1 * (3 * ti2 * t) + p2 * (3 * ti * t2) + p3 * t3);
}
public void ElementWiseMaxSelf(vector v)
{
if (v.X > X)
{
X = v.X;
}
if (v.Y > Y)
{
Y = v.Y;
}
}
public void ElementWiseMinSelf(vector v)
{
if (v.X < X)
{
X = v.X;
}
if (v.Y < Y)
{
Y = v.Y;
}
}
public bool Intersects(volume obb2)
{
volume obb1;
if (this.IsAabb)
{
obb1 = obb2;
obb2 = this;
}
else
{
obb1 = this;
}
var d = new vector();
var v = obb1.Center - obb2.Center;
var eax = obb2.Ax * obb2.Extents.X;
var eay = obb2.Ay * obb2.Extents.Y;
var e1 = eax + eay;
var e2 = eay - eax;
d.X = Math.Abs(obb1.Ax.Dot(e1));
d.Y = Math.Abs(obb1.Ax.Dot(e2));
if (obb1.Extents.X + d.Max() < Math.Abs(obb1.Ax.Dot(v)))
{
return(false);
}
d.X = Math.Abs(obb1.Ay.Dot(e1));
d.Y = Math.Abs(obb1.Ay.Dot(e2));
if (obb1.Extents.Y + d.Max() < Math.Abs(obb1.Ay.Dot(v)))
{
return(false);
}
eax = obb1.Ax * obb1.Extents.X;
eay = obb1.Ay * obb1.Extents.Y;
e1 = eax + eay;
e2 = eay - eax;
d.X = Math.Abs(obb2.Ax.Dot(e1));
d.Y = Math.Abs(obb2.Ax.Dot(e2));
if (obb2.Extents.X + d.Max() < Math.Abs(obb2.Ax.Dot(v)))
{
return(false);
}
d.X = Math.Abs(obb2.Ay.Dot(e1));
d.Y = Math.Abs(obb2.Ay.Dot(e2));
if (obb2.Extents.Y + d.Max() < Math.Abs(obb2.Ay.Dot(v)))
{
return(false);
}
return(true);
}
static bool PointInTriangle(vector2 p1, vector2 p2, vector2 p3, vector2 check)
{
var v1 = check - p1;
var v2 = check - p2;
var v3 = check - p3;
var result1 = Side(v1, v2);
var result2 = Side(v2, v3);
var result3 = Side(v3, v1);
return(result1 == result2 && result2 == result3);
}
public Range2d(vector min, vector max, bool normalize)
{
if (normalize)
{
vector.ElementWiseMinMax(min, max, out Min, out Max);
}
else
{
Min = min;
Max = max;
}
}
static public vector ElementWiseMax(vector v1, vector v2)
{
if (v2.X < v1.X)
{
v2.X = v1.X;
}
if (v2.Y < v1.Y)
{
v2.Y = v1.Y;
}
return(v2);
}
public Range2d(IEnumerable <vector> positions)
{
vector min = vector.MaxValue, max = vector.MinValue;
foreach (var p in positions)
{
min.ElementWiseMinSelf(p);
max.ElementWiseMaxSelf(p);
}
Min = min;
Max = max;
}
public Range2d(IEnumerable <volume> volumes)
{
vector min = vector.MaxValue, max = vector.MinValue;
foreach (var v in volumes)
{
min.ElementWiseMinSelf(v.Min);
max.ElementWiseMaxSelf(v.Max);
}
Min = min;
Max = max;
}
static int Side(vector2 v1, vector2 v2)
{
var a = v1.X * v2.Y - v1.Y * v2.X;
if (a < 0)
{
return(-1);
}
if (0 < a)
{
return(1);
}
return(0);
}
public static void ElementWiseMinMax(vector v1, vector v2, out vector min, out vector max)
{
if (v2.X < v1.X)
{
var t = v1.X; v1.X = v2.X; v2.X = t;
}
;
if (v2.Y < v1.Y)
{
var t = v1.Y; v1.Y = v2.Y; v2.Y = t;
}
;
min = v1;
max = v2;
}
public vector this[int index] {
get {
switch (index)
{
case 0:
return(P0);
case 1:
return(P1);
case 2:
return(P2);
case 3:
return(P3);
default:
throw new NotImplementedException();
}
}
set {
switch (index)
{
case 0:
P0 = value;
break;
case 1:
P1 = value;
break;
case 2:
P2 = value;
break;
case 3:
P3 = value;
break;
default:
throw new NotImplementedException();
}
}
}
public void ClipSelf(vector min, vector max)
{
if (X < min.X)
{
X = min.X;
}
else if (max.X < X)
{
X = max.X;
}
if (Y < min.Y)
{
Y = min.Y;
}
else if (max.Y < Y)
{
Y = max.Y;
}
}
public bool LessIdThan(vector v)
{
if (X < v.X)
{
return(true);
}
if (X > v.X)
{
return(false);
}
if (Y < v.Y)
{
return(true);
}
if (Y > v.Y)
{
return(false);
}
return(false);
}
public vector Clip(vector min, vector max)
{
vector v = this;
if (v.X < min.X)
{
v.X = min.X;
}
else if (max.X < v.X)
{
v.X = max.X;
}
if (v.Y < min.Y)
{
v.Y = min.Y;
}
else if (max.Y < v.Y)
{
v.Y = max.Y;
}
return(v);
}
/// <summary>
/// Use Newton-Raphson iteration to find better root.
/// </summary>
/// <param name="Q">Current fitted curve</param>
/// <param name="P">Digitized point</param>
/// <param name="u">Parameter value for <see cref="P"/></param>
/// <returns>パラメータ</returns>
static element NewtonRaphsonRootFind(cubicbezier Q, vector P, element u)
{
/* Compute Q(u) */
var Q_u = Q.Interpolate(u);
/* Generate control vertices for Q' */
var Q1 = new vector[3]; /* Q' and Q'' */
for (int i = 0; i <= 2; i++)
{
Q1[i] = (Q[i + 1] - Q[i]) * 3;
}
/* Generate control vertices for Q'' */
var Q2 = new vector[2];
for (int i = 0; i <= 1; i++)
{
Q2[i] = (Q1[i + 1] - Q1[i]) * 2;
}
/* Compute Q'(u) and Q''(u) */
var Q1_u = Interpolate2(u, Q1[0], Q1[1], Q1[2]);
var Q2_u = Interpolate1(u, Q2[0], Q2[1]);
/* Compute f(u)/f'(u) */
var Q_u_P = Q_u - P;
var numerator = Q_u_P.Dot(Q1_u);
var denominator = Q1_u.LengthSquare + Q_u_P.Dot(Q2_u);
if (denominator == 0)
{
return(u);
}
/* u = u - f(u)/f'(u) */
return(u - numerator / denominator);
}
public volume Expand(vector v)
{
return(new volume(Min - v, Max + v));
}
public bool Contains(vector v)
{
v.SubSelf(Center);
v = (Ax * v.X) + (Ay * v.Y);
return(Math.Abs(v.X) <= Extents.X && Math.Abs(v.Y) <= Extents.Y);
}
public Aabb2d(Aabb2f v)
{
Center = new vector(v.Center);
Extents = new vector(v.Extents);
}
public Aabb2d(vector center, vector extents)
{
Center = center;
Extents = extents;
}
public Range2d(Range2f v)
{
Min = new vector(v.Min);
Max = new vector(v.Max);
}
public Range2d(vector min, vector max)
{
Min = min;
Max = max;
}
public Range2d(vector position)
{
Min = position;
Max = position;
}
public void ExpandSelf(vector v)
{
Min.SubSelf(v);
Max.AddSelf(v);
}
public volume Merge(vector v)
{
return(new volume(vector.ElementWiseMin(Min, v), vector.ElementWiseMax(Max, v)));
}
public void MergeSelf(vector v)
{
Min.ElementWiseMinSelf(v);
Max.ElementWiseMaxSelf(v);
}