Coffeehouse Thread
15 postsCan someone check my math?

Edit: Added Translate function, fixed parameters
Hey, I'm trying to implement the cubic bezier curve for an animation, I found the definition below from wikipedia, can someone validate this for me?
public float CubicBezier(float t, PointF p0, PointF p1, PointF p2, PointF p3) { if (t < 0  t > 1) throw new ArgumentException(); PointF b = Translate( Scale(Power(1  t, 3), p0), Scale(3 * Power(1  t, 2) * t, p1), Scale(3 * (1  t) * Power(t, 2), p2), Scale(Power(t, 3), p3) ); return b.Y; } public float Power(float n, float p) { double v = Math.Pow((double) n, (double) p); return Convert.ToSingle(v); } public PointF Scale(float f, PointF p) { PointF ps = new PointF(); ps.X = p.X * f; ps.Y = p.Y * f; return ps; } public PointF Translate(params PointF[] ps) { PointF pt = new PointF(); foreach (PointF p in ps) { pt.X = pt.X + p.X; pt.Y = pt.Y + p.Y; } return pt; }

BRIAAAAAAAAAN!!! HELP!!

Shouldn't your return value a point? like return b?
Also I would think it is better doing it recursively? I mean, this way you can support higher order curves and the calculation is much more straight forward.

public PointF CubicBezier(float t, PointF p0, PointF p1, PointF p2, PointF p3) { float cx = 3 * (p1.X  p0.X); float bx = 3 * (p2.X  p1.X)  cx; float ax = p3.X  p0.X  cx  bx; float cy = 3 * (p1.Y  p0.Y); float by = 3 * (p2.Y  p1.Y)  cy; float ay = p3.Y  p0.Y  cy  by; float tCubed = t * t * t; float tSquared = t * t; float resultX = (ax * tCubed) + (bx * tSquared) + (cx * t) + p0.X; float resultY = (ay * tCubed) + (by * tSquared) + (cy * t) + p0.Y; return new PointF(resultX, resultY); }

I like Tokter's solution. The reason I only return the Y value is that I assume X = t. Maybe that won't be the case. I'll have to play around to check.
Thanks everybody

15 minutes ago, Minh wrote
I like Tokter's solution. The reason I only return the Y value is that I assume X = t. Maybe that won't be the case. I'll have to play around to check.
Thanks everybody
Nope, t is from 0 to 1, not X.
The easy solution is,
private Point InBetweenAB(double t, Point A, Point B)
{
return new Point((1  t) * A.X + t * B.X, (1  t) * A.Y + t * B.Y);
}
private Point[] OneLessOrder(double t, Point[] points)
{
Point[] result = new Point[points.Length  1];for (int i = 0; i < result.Length; i++)
result[i] = InBetweenAB(t, points[i], points[i + 1]);return result;
}
public Point MultiCurve(double t, Point[] points)
{
if (points==null  points.Length <= 0)
return null;
Point[] result = points;
while (result.Length > 1)
result = OneLessOrder(t, result);
return result[0];
}Ok, this is strange, the insert code block doesn't work. I am using your own code block and pasted my code. So, the line number maybe off. (that also doesn't work). So, I am just having the text here.
this should do it.
obviously slower, but, it works for any number of control points. And the code is quite brainless.

@magicalclick, Ah, I see. I'm framing the points inside (0,0) and (1,1) anyways, so I could use t as X, but I can see how that's confusing.
I'm not sure your code displayed in its entirity

18 minutes ago, Minh wrote
@magicalclick, Ah, I see. I'm framing the points inside (0,0) and (1,1) anyways, so I could use t as X, but I can see how that's confusing.
I'm not sure your code displayed in its entirity
In your case, x = t IFF the points for X direction are monotonically increasing at exact same speed. Meaning your points needs to be,
Point1 X = 0
Point2 X = 0.3333333
Point3 X = 0.6666666
Point4 X = 1
otherwise the speed of the animation along X axis will be whacky. Also if you have Point 3 X = 1 and Point4 X = 0.66666, then, your path will be wrong.
..........
You meaning you didn't see my code? I can see it on my PC. Didn't test out my code, but, should work.

1 hour ago, Minh wrote
Tokter,
Looking more into it, your routine isn't a direct reflection of this formula:
Can you point me to how you worked that out?
First you get the extended form of your formula http://www.wolframalpha.com/input/?i=%281t%29%5E3*P0%2B3*%281t%29%5E2*t*P1%2B3*%281t%29*t%5E2*P2%2Bt%5E3*P3:
P0*t^3 + 3*P0*t^2  3*P0*t + P0 + 3*P1*t^3  6*P1*t^2 + 3*P1*t  3*P2*t^3 + 3*P2*t^2 + P3*t^3
Then you factorize for t^3, t^2 and t
t^3(P0 + 3*P1  3*P2 + P3) + t^2(3*P0  6*P1 + 3*P2) + t(3*P1  3* P0) + P0
then you substitute:
c = 3*(P1  P0)
b = 3*(P2  P1)  c
a = P3  P0  c bAnd you get:
B(t) = (a * t^3) + (b * t^2) + (c * t) + P0

Isn't it something like the following C#
PointF B(double t,PointF P0, PointF P1, PointF P2, PointF P3) { return New PointF(B(t, P0.X, P1.X, P2.X, P3.X),B(t, P0.Y, P1.Y, P2.Y, P3.Y)) } double B(double t,double P0, double P1,double P2, double P2) { if( 0 <= t && t <= 1) { double a = (1  t); double b = 3 * a; return (a^3 * P0) + (b^2 * t * P1) + (b * t^2 * P2) + (t^3 * P3); } else { throw new ArgumentOutOfRangeException("t"); } }

(b^2 * t * P1):
b^2 = (3*(1t))^2 = 9(1t)^2 instead of 3(1t)^2
so it should be (3 * a^2 * t * P1) imho

@magicalclick:You meaning you didn't see my code? I can see it on my PC. Didn't test out my code, but, should work.
Oh I see the code now... I was confused about how OneLessOrder and MultiCurve relate to the Bezier 
@Tokter, I'll take your word for it lol Wolfram Alpha couldn't figure it out without a pro account

10 minutes ago, Minh wrote
@magicalclick:You meaning you didn't see my code? I can see it on my PC. Didn't test out my code, but, should work.
Oh I see the code now... I was confused about how OneLessOrder and MultiCurve relate to the BezierOh that, as you can see, you can have K level of control points, OneLessOrder just reduce the level by 1. You keep doing it until the level is 1. That's how Bezier Curve works at its most basic form.
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