Dynamic bezier curve creation C++ - c++

I'm trying to imitate the drawing of lines in a certain iOS game on cocos2dx,
The way i chose to implement it is by creating a dynamic cubic bezier curve.
For that, i will have to get 4 x-y screen locations:
1) begin point
2) control point 1
3) control point 2
4) ending point
As for the begin and end points, it's obvious i should use onTouchBegan and onTouchEnded and retrieve the relevant locations.
Since the line should be drawn immediately meaning, not drawing the non processed line and then process it, but creating a temp bezier curve at any time, i don't really know how to approach it and create the curve.
onTouchMoved(cocos2d::Touch *Touch, cocos2d::Event *Event)
is the problematic part, how do i determine the relevant control points?
any suggestions or ideas for different implementation will be welcomed.
Cheers.

Related

Drawing application with OpenGL/Openframeworks

I'm trying to program a brush stroke/drawing application using OpenGL within Openframeworks. For now I'm just trying to create squiggly lines that follow your mouse.
I've started by using ofpolyline but I have just managed to create a straight line that follows my mouse. I would really appreciate some pseudo code or something to point me in the right direction.
start. set (mouseX,mouseY);
end.set(mouseX,mouseY);
ofPolyline myline;
myline.addVertex(start.x,start.y);
myline.curveTo(end.x,end.y);
myline.bezierTo(mouseX,mouseY, mouseX,mouseY,mouseX, mouseY);
myline.addVertex(end.x,end.y);
myline.draw();
A Bezier curve with two vertices is always just a straight line segment. You need to add more vertices/control points to get non-degenerate (round) curves. So you could store the last mouse position somewhere, and add a new vertex when the mouse was moved by a certain amount (eg 20 pixels). Or add a vertex when the user clicks. However, if you always just call bezierTo(x,y,x,y,x,y), you will still only get straight lines. You need to offset the two control points from (x,y) to get round curves.

Draw a bezier curve(s) with a set of points from a vector

I was wondering what would be the best and less complicated way of drawing a bezier curve in c++ with a set of points (roughly 100+ points) that are stored inside a vector
From my understanding:
-Bezier curves consist of 4 control points, the points in the middle dictate the direction/tangent of the curve
Would one possible method be to breakdown the points into different segments and from each segment determine the control points and tangents?
It is called a cubic spline and if you search you might find some C++ code for it. I used the free Fortran code from Numerical Recipes Online and ported it to C# with no problems.
Would one possible method be to
breakdown the points into different
segments and from each segment
determine the control points and
tangents?
Yes, basically one connects the line segments end-to-end such that the slope approaching the end of the line segment is equal on both sides of the connection point. This is called a cubic spline. You can find algorithms for this here.

Finding object under mouse

I'm developing a game that basically has its entire terrain made out of AABB boxes. I know the verticies, minimum, and maximum of each box. I also set up my camera like this:
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(Camera.rotx,1,0,0);
glRotatef(Camera.roty,0,1,0);
glRotatef(Camera.rotz,0,0,1);
glTranslatef(-Camera.x,-Camera.y,-Camera.z);
What I'm trying to do is basically find the cube the mouse is on. I thought about giving the mouse position a forward directional vector and simply iterating through until the 'mouse bullet' hits something. However this envolves interating through all objects several times. Is there a way I could do it by only iterating through all the objects once?
Thanks
This is usually referred to as 'picking' This here looks like a good gl based link
If that is tldr, then a basic algorithm you could use
sort objects by z (or keep them sorted by z, or depth buffer tricks etc)
iterate and do a bounds test, stopping when you hit the first one.
This is called Ray Tracing (oops, my mistake, it's actually Ray Casting). Every Physics engine has this functionality. You can look at one of the simplest - ODE, or it's derivative - Bullet. They are open-source so you can take out what you don't need. They both have a handy math library that handles all oftenly needed matrix and vertex operations.
They all have demos on how to do exactly this task.
I suggest you consider looking at this issue from a bigger perspective.
The boxes are just points at a lower resolution. The trick is to reduce the resolution of the mouse to figure out which box it is on.
You may have to perform a 2d to 3d conversion (or vice versa). In most games, the mouse lives in a 2d coordinate world. The stuff "under" the mouse is a 2d projection of a 3d universe.
You want to use a 3D picking algorithm. The idea is that you draw a ray from the user's position in the virtual world in the direction of the click. This blog post explains very clearly how to implement such an algorithm. Essentially your screen coordinates need to be transformed from the screen space to the virtual world space. There's a website that has a very good description about the various transformations involved and I can't post the link due to my rank. Search for book of hook's mouse picking algorithm [I do not own the site and I haven't authored the document].
Once you get a ray in the desired direction, you need to perform tests for intersection with the geometries in the real world. Since you have AABB boxes entirely, you can use simple vector equations to check which geometry intersects the ray. I would say that approximating your boxes as a sphere would make life very easy since there is a very simple sphere-ray intersection test. So, your ray would be described by what you obtain from the first step (the ray drawn in the first step) and then you would need to use an intersection test. If you're ok with using spheres, the center of the sphere would be the point you draw your box and the diameter would be the width of your box.
Good Luck!

How do bezier handles work?

On Wikipedia I found information about bezier curves and made a function to generate the inbetween points for a bezier polygon. I noticed that Expression Design uses bezier handles. This allows a circle to be made with 4 points each with a bezier handle.
I'm just not sure mathematically how this works in relation with the formula for bezier point at time T. How do these handle vectors work to modify the shape? Basically what's there relation to the bezier formula?
Thanks
Basically, the 4 points used in the cubic bezier formula are the 2 points the curve is between, plus the two points of the handles on that "side" of the first two points (1 handle from each of the first points). If there are double handles on each point, the handles on the "opposite" side of the points from the curve currently being calculated are ignored (they're used for generating the curve that comes out of the opposite side).
The actual generation method used for cubic bezier curves is outlined on the Wikipedia page you linked in your question.
The 4 points of a Bezier segment are the two endpoints of the segment and two handles, one per endpoint. The handles determine the initial direction of the line as it leaves the endpoint. The distance from the handle to the endpoint determines the amount of "pull" that the handle exerts on the path.
Often you will find multiple Beziers connected end to end, with the endpoint of one being shared as the starting point of the next. This guarantees an unbroken curve. If the handles on either side of a point are directly across from each other, the angle at the joint will match up; if the handles are also the same distance from the point, the angle will be completely smooth and there will not be a visible discontinuity at the point.
An interesting property of Bezier segments is that the curve will fit entirely within the parallelogram defined by the 4 points.
What I have been describing is the most common form of Bezier, the cubic. There is also a quadratic which only has a single handle between the two endpoints; the most common application is TrueType fonts.

Drawing a Smooth Line from Tablet Input

As the user drags their stylus across the tablet, you receive a series of coordinates. You want to approximate the pen's path with a smooth line, trailing only a few sample points behind it. How would you do this?
In other words, how would you render a nice smooth responsive line as a user draws it with their tablet? Simply connecting the dots with straight lines is not good enough. Real drawing programs do a much better job of curving the line, no matter how close or far the sample points are. Some even let you give them a number to indicate the amount of smoothing to be done, accounting for jittery pens and hands. Where can I learn to do this stuff?
I know this is an old question but I had the same problem and I came with 2 different solutions:
The first approach is use two resolutions: One , when the user is inserting the path points connecting them with straight lines. Two , when the user finish the stroke delete the lines and draw the spline over. That should be smoother than the straight lines.
The second approach it is to smooth the new points with a weighted mean of the sampled points. So each time you get a new point [x1,y1] instead of painting it directly, you take the previous points [x2,y2] and create a new intermediate point with the weighted mean of the two points. The pseudocode could be something like:
newPoint = [x1,y1];
oldPoint = [x2,y2];
point2Paint = [(x1*0.3) + (x2*0.7), (y1*0.3) + (y2*0.7)];
oldPoint= newPoint;
Being 0.7 and 0.3 the coefficients for the weighted mean ( You can change them to get your desired smoothing :)
I hope this would help
UPDATE Dec 13: Here it is an article explaining different drawing methods, there are good concepts that can be applied (edge smoothing, bezier curves, smooth joints)
http://perfectionkills.com/exploring-canvas-drawing-techniques
I never had to implement these (only for academic purposes), but you may want to take a look at wikipedia's interpolation article.
Extracted from the article:
interpolation is a method of constructing new data points within the range of a discrete set of known data points.
In engineering and science one often has a number of data points, as obtained by sampling or experimentation, and tries to construct a function which closely fits those data points. This is called curve fitting or regression analysis. Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points.
Hope it helps.