Bezier Curve to Triangle Strip

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So, I don't normally do this but since it's been about 3 hours since I posted my other thread and no one has even LOOKED at it (has 0 views), I decided to repost my question here.

Basically, I have a vector2 array of points that are currently being drawn as a line list. But I want to add thickness to them. The only way I see myself being able to do this is creating a curve "parallel" to the first curve in which each point is equidistant from the opposing point. Then, I'd convert the 2 curves into a triangle list by alternating through the points.

My problem is in calculating a parallel curve.

So does anyone know how to do this OR do you know how to add thickness to a line in XNA? Thanks in advance. ^^

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So I think I got a way to do it... since a curve is technically a bunch of straight lines, you could add thickness by adding points above and bellow a point along a perpendicular line. My function isn't working correctly. Anyone know why?

public static Vector2 perpendicularPoint(Vector2 p1, Vector2 p2) { float m = (p1.Y - p2.Y) / (p1.X - p2.Y); float b = p1.Y - ((1 / m) * p1.X); Vector2 point = new Vector2(0, ; if (point == p1) { point = new Vector2(-1, b + (-1 / m)); } return point; } ///And this function is used to calculate the exact points. You plug in a point, a point on the perpendicular line, and a distance to travel. public static Vector2 distanceToPoint(Vector2 MoveFrom, Vector2 Reference, int toTravel) { //get distance //sqrt( (X2 - X1)^2 + (y2 - y1)^2 ) = d float d = (int)Math.Sqrt((Math.Pow((MoveFrom.X - Reference.X), 2) + Math.Pow((MoveFrom.Y - Reference.Y), 2))); //Get X and Y differences float difX = MoveFrom.X - Reference.X; float difY = MoveFrom.Y - Reference.Y; //Get Ratio float ratio = ((float)toTravel / d); //Apply ratio to differences difX = difX * ratio; difY = difY * ratio; //Return new Vector return new Vector2(MoveFrom.X + difX, MoveFrom.Y + difY); } 

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Cross posting is not a good idea. I posted in your other thread.

And I said that "isn't working correctly" doesn't mean ANYTHING (a sticky should be made on this thing, it's pretty annoying to always ask for more info)

Anyways: post an image to make our task easier.

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Cross posting is not a good idea. I posted in your other thread.

And I said that "isn't working correctly" doesn't mean ANYTHING (a sticky should be made on this thing, it's pretty annoying to always ask for more info)

Anyways: post an image to make our task easier.

As the curve approaches the middle of the screen, the thickness decreases.

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perpendicular vector:

xp = y
yp = -x

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perpendicular vector:

xp = y
yp = -x

That doesn't work. It doesn't even incorporate the second point. How can you calculate a perpendicular point with just one point o.O

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I wrote vector, not point. I meant direction.

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I wrote vector, not point. I meant direction.

Even so, you can't calculate direction with one point.

Here, what is xp ,yp, x, and y?

Cause the way I see it is xp, yp are the x and y direction of the vector and x and y are 1 points coords...

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[quote name='szecs' timestamp='1298215675' post='4776689']
I wrote vector, not point. I meant direction.

Even so, you can't calculate direction with one point.

Here, what is xp ,yp, x, and y?

Cause the way I see it is xp, yp are the x and y direction of the vector and x and y are 1 points coords...
[/quote]
szecs is right about using the perpendicular vector. The vector that this vector is perpendicular to would be the unit-length direction (tangent) vector at the specified point on the spline, which can be computed using some simple vector math if the spline is represented as a series of line segments, or can be computed directly from the spline representation.

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[quote name='slynk' timestamp='1298218986' post='4776705']
[quote name='szecs' timestamp='1298215675' post='4776689']
I wrote vector, not point. I meant direction.

Even so, you can't calculate direction with one point.

Here, what is xp ,yp, x, and y?

Cause the way I see it is xp, yp are the x and y direction of the vector and x and y are 1 points coords...
[/quote]
szecs is right about using the perpendicular vector. The vector that this vector is perpendicular to would be the unit-length direction (tangent) vector at the specified point on the spline, which can be computed using some simple vector math if the spline is represented as a series of line segments, or can be computed directly from the spline representation.
[/quote]

Ohhhhhhh.... is X, Y supposed to be the direction of the line? And xp, yp is the perpendicular direction? That would be where my confusion arose. I could get how you can calculate a perpendicular direction without two points representing the line XD.

Also, does my distance function look right?

I was trying to make a function that give two points and a distance, would move from the starting point a certain distance. I guess I'll switch it to a point and a directional vector instead.

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Fixed it, the directional vector worked. Thanks so much ^^

Anyone who comes upon this, here's some working code to create a bezier curve and then convert it into a trianglestrip that is "thickness" wide. ^^

 public const int SUBDIVISIONS = 30; public const int THICKNESS = 30; public static Color UNLIT = Color.Black; /* * Given 2 points and 2 control points, this function will calculate a curve */ public static VertexPositionColor[] bezierCurve(Vector2 start, Vector2 end, Vector2 c1, Vector2 c2) { VertexPositionColor[] points = new VertexPositionColor[SUBDIVISIONS + 2]; float fraction; for (int i = 0; i < SUBDIVISIONS + 2; i++) { fraction = i * (1f / (float)SUBDIVISIONS); points = new VertexPositionColor(new Vector3((float)((start.X * Math.Pow((1 - fraction), 3)) +(c1.X * 3 * fraction * Math.Pow(1-fraction, 2)) +(c2.X * 3 * Math.Pow(fraction,2) * (1-fraction)) +(end.X * Math.Pow(fraction,3))), (float)((start.Y * Math.Pow((1 - fraction), 3)) + (c1.Y * 3 * fraction * Math.Pow(1 - fraction, 2)) + (c2.Y * 3 * Math.Pow(fraction, 2) * (1 - fraction)) + (end.Y * Math.Pow(fraction, 3))), 0), UNLIT); } return points; } /* * This function treats the curve as a serious of straight lines and calculates points on a line perpendicular to each point, resulting in two points THICKNESS appart. * Requires THICKNESS to be set */ public static VertexPositionColor[] curveToStrip(VertexPositionColor[] curve) { VertexPositionColor[] strip = new VertexPositionColor[curve.Length * 2]; VertexPositionColor[] new1 = new VertexPositionColor[curve.Length]; VertexPositionColor[] new2 = new VertexPositionColor[curve.Length]; for (int i = 0; i < curve.Length; i++) { if (i < curve.Length-1) { Vector2 p1 = new Vector2(curve.Position.X, curve.Position.Y); Vector2 p2 = new Vector2(curve[i + 1].Position.X, curve[i + 1].Position.Y); Vector2 perpPoint = perpendicularPoint(p1, p2); new1 = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, THICKNESS / 2), 0), UNLIT); new2 = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, -1 * THICKNESS / 2), 0), UNLIT); } else { Vector2 p1 = new Vector2(curve.Position.X, curve.Position.Y); Vector2 p2 = new Vector2(curve[i - 1].Position.X, curve[i - 1].Position.Y); Vector2 perpPoint = perpendicularPoint(p1, p2); new1 = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, -1 * THICKNESS / 2), 0), UNLIT); new2 = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, THICKNESS / 2), 0), UNLIT); } } //strip[0] = new1[0]; //strip[1] = new2[0]; for (int i = 0; i < curve.Length; i++) { strip[i * 2] = new2; strip[(i * 2) + 1] = new1; } return strip; } public static Vector2 perpendicularPoint(Vector2 p1, Vector2 p2) { return new Vector2(p2.Y - p1.Y, -1 * (p2.X - p1.X)); } public static Vector2 distanceToPoint(Vector2 MoveFrom, Vector2 Direction, int toTravel) { //Make a point Vector2 Reference = new Vector2(MoveFrom.X + Direction.X, MoveFrom.Y + Direction.Y); //get distance //sqrt( (X2 - X1)^2 + (y2 - y1)^2 ) = d float d = (int)Math.Sqrt((Math.Pow((MoveFrom.X - Reference.X), 2) + Math.Pow((MoveFrom.Y - Reference.Y), 2))); //Get X and Y differences float difX = MoveFrom.X - Reference.X; float difY = MoveFrom.Y - Reference.Y; //Get Ratio float ratio = -1 *((float)toTravel / d); //Apply ratio to differences difX = difX * ratio; difY = difY * ratio; //Return new Vector return new Vector2(MoveFrom.X + difX, MoveFrom.Y + difY); } }