Sign in to follow this  
slynk

Bezier Curve to Triangle Strip

Recommended Posts

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.

[url="http://www.gamedev.net/topic/595833-adding-thickness-to-bezier-curve/"]http://www.gamedev.net/topic/595833-adding-thickness-to-bezier-curve/[/url]

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. ^^

Share this post


Link to post
Share on other sites
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?

[code]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, B);

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);
}


[/code]

Share this post


Link to post
Share on other sites
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.

Share this post


Link to post
Share on other sites
[quote name='szecs' timestamp='1298100706' post='4776237']
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.
[/quote]

[img]http://i1100.photobucket.com/albums/g401/gamersjd2002/curve.png[/img]


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

Share this post


Link to post
Share on other sites
[quote name='szecs' timestamp='1298196852' post='4776620']
perpendicular vector:

xp = y
yp = -x
[/quote]

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

Share this post


Link to post
Share on other sites
[quote name='szecs' timestamp='1298215675' post='4776689']
I wrote vector, not point. I meant direction.
[/quote]

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...

Share this post


Link to post
Share on other sites
[quote name='slynk' timestamp='1298218986' post='4776705']
[quote name='szecs' timestamp='1298215675' post='4776689']
I wrote vector, not point. I meant direction.
[/quote]

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.

Share this post


Link to post
Share on other sites
[quote name='jyk' timestamp='1298234377' post='4776781']
[quote name='slynk' timestamp='1298218986' post='4776705']
[quote name='szecs' timestamp='1298215675' post='4776689']
I wrote vector, not point. I meant direction.
[/quote]

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.

Share this post


Link to post
Share on other sites
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. ^^

[code] 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[i] = 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[i].Position.X, curve[i].Position.Y);
Vector2 p2 = new Vector2(curve[i + 1].Position.X, curve[i + 1].Position.Y);
Vector2 perpPoint = perpendicularPoint(p1, p2);

new1[i] = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, THICKNESS / 2), 0), UNLIT);
new2[i] = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, -1 * THICKNESS / 2), 0), UNLIT);
}
else
{
Vector2 p1 = new Vector2(curve[i].Position.X, curve[i].Position.Y);
Vector2 p2 = new Vector2(curve[i - 1].Position.X, curve[i - 1].Position.Y);
Vector2 perpPoint = perpendicularPoint(p1, p2);

new1[i] = new VertexPositionColor(new Vector3(distanceToPoint(p1, perpPoint, -1 * THICKNESS / 2), 0), UNLIT);
new2[i] = 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[i];
strip[(i * 2) + 1] = new1[i];
}

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);
} }[/code]

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this