I have a start point Double2D startPoint and a ArrayList of Line2D Objekts.
Now i want to calc the min distance from point to the line and return the intersection point.
Related
Given a large bunch of points in 2D and a reference point x_0, in order to find the closest (couple of) points to x_0, i.e. distance d, I could calculate the distance of each point from x_0 using Euclidean distance formula. The formula however needs taking a square root, which is computationally expensive. Would I get the same result if I'd just calculate the square of the distance d^2 and choose the points with lowest d^2? I'm not interested in the real distance, just in the relative ordering.
The aim of my work is given in the algorithm below.
Initialize the H/W; wait until GPS module has a valid fix and then start the motor.
Get actual position from the GPS.
Calculate the distance and heading information to the next waypoint.
Compare the actual heading with the current heading angle and feed the difference to the motors.
When the actual position is close to the first waypoint, switch to the next waypoint.
If/when the last waypoint is reached, stop the motor.
If not go to step 2.
I'm calculating the distance between a pre-defined coordinate and the current location using Haversine formula. I need heading angle for the same pair of coordinates. But when I use the atan2 formula and compile using the Arduino IDE, I am getting the angle as 0.05,0.03. Am I doing it wrong? can the heading angle be calculated for points within a proximity of 10m?
formula
double y = sin(dlon) * cos(lat2);
double x = ((cos(lat1) * sin(lat2)) - (sin(lat1) * cos(lat2) * cos(dlon)));
double brng = atan2(y, x);
I'm making a program in which many weird shapes are drawn onto a canvas. Right now i'm trying to implement the last, and possebly hardest, one.
In this particular shape i need a way to find the location (on a 2d canvas) where the line hits the shape. The following image is an example of what i have right now.
The black dots are the points that a known to me (i also have the location of the center of the three open circles and the radius of these circles). Each of the three outer lines needs a line towards the center dot, ending at the point that it hits the circle. This shape can be turned 90, 180 or 270 degrees.
The shape should look something like the following:
If you need any other information, please ask me in the comments. I'm not very good at math so please be gentle, thanks!
If A and B are points forming a line, then you can describe any point on that line using coordinates:
x = t·Ax + (1−t)·Bx
y = t·Ay + (1−t)·By
0 ≤ t ≤ 1
You can also describe the circle with center M and radius r as
(x − Mx)2 + (y − My)2 = r2
So take the x and y from the equations of the line, and plug them into the equation of the circle. You obtain a quadratic equation in t. Its two solutions describe the two points of intersection between the line and circle. In your example, only one of them lies on the line segment, i.e. satisfies 0 ≤ t ≤ 1. The other describes a point on the extension of the segment past its endpoint. Take the correct value for t back to the equations of the line, and you obtain the x and y coordinates of the point of intersection.
If you don't know up front which circle you want to intersect with a given line, then intersect all three and choose the most appropriate point afterwards. Probably that is the point closest to the outside starting point of the line segment. The same goes in cases where both points of intersection lie on the segment.
Working with iPhone and Objective C.
I am working on a game and I need to correctly reflect a ball off a circle object. I am trying to do it as a line and circle intersection. I have my ball position outside the circle and I have the new ball position that would be inside the circle at the next draw update. I know the intersect point of the line (ball path) and the circle. Now I want to rotate the ending point of the ball path about the intersection point to get the correct angle of reflection off the tangent.
The following are known:
ball current x,y
ball end x,y
ball radius
circle center x,y
circle radius
intersection point of ball path and circle x and y
I know I need to find the angle of incidence between the tangent line and the incoming ball path which will also equal my angle of reflection. I think once I know those two angles I can subtract them from 180 to get my rotation angle then rotate my end point about the angle of intersection by that amount. I just don't know how.
First, you should note that the center of the ball doesn't have to be inside of the circle to indicate that there's a reflection or bounce. As long as the distance between ball center and circle is less than the radius of the ball, there will be a bounce.
If the radius of the circle is R and the radius of the ball is r, things are simplified if you convert to the case where the circle has radius R+r and the ball has radius 0. For the purposes of collision detection and reflection/bouncing, this is equivalent.
If you have the point of intersection between the (enlarged) circle and the ball's path, you can easily compute the normal N to the circle at that point (it is the unit vector in the direction from the center of the circle to the collision point).
For an incoming vector V the reflected vector is V-2(N⋅V) N, where (N⋅V) is the dot product. For this problem, the incoming vector V is the vector from the intersection point to the point inside the circle.
As for the reflection formula given above, it is relatively easy to derive using vector math, but you can also Google search terms like "calculate reflection vector". The signs in the formula will vary with the assumed directions of V and N. Mathworld has a derivation although, as noted, the signs are different.
I only know the solution to the geometry part.
Let:
r1 => Radius of ball
r2 => Radius of circle
You can calculate the distance between the two circles by using Pythagoras theorem.
If the distance is less than the r1+r2 then do the collision.
For the collision,I would refer you Here. It's in python but I think it should give you an idea of what to do. Hopefully, even implement it in Objective C. The Tutorial By PeterCollingRidge.
Given a starting point, a heading, a distance, and a line segment, find the first point along this heading that is the specified distance away from this line segment.
I covered two cases, but I haven't been able to cover the last one.
First case: heading away from the line. Ignore it even if the starting point is within the specified distance.
Second case: It intersects the line. I solved it using trig and triangles. Initially didn't consider the next case.
Third case: It is heading towards the line, but it does not intersect it. I think this will solve the second case as well if it's done correctly.
Three subcases:
The minimum line distance is greater than the specified distance. Ignore it.
The minimum line distance is equal to the specified distance. Found the points already.
The minimum line distance is less than the specified distance. This means there is a perpendicular line from the along the heading to an endpoint of the line segment that is less than the distance needed. This also means that on either side of this perpendicular line will be two lines of the distance needed. One is perpendicular to the heading, while the other is closest to the same endpoint and not perpendicular to the heading. Just a matter of finding those points and seeing which one is closer to the start point.
This is where I am stuck today. Drawing it up was easy, but doing the vector calc or whatever turned out tricky.
It's possible to rephrase this as:
At what time(s) is P(t) = P0 + t*v at a distance D from the line segment L((x1,y1), (x2,y2))?
v=(sin(heading), -cos(heading)) in my case.
Shoot mang your solution doesn't always work. I found a counter example:
Line Segment = (0,0) -> (0,14)
Start Point = (19, 6) # heading -159.5 or 200.5 in west/counter-clockwise
It will intersect the line at (2.952, 0.0) so I ask, where does it it come within a distance of 0.0.
The result I get is incorrect.
http://img5.imageshack.us/i/failuref.png/
How I can tell which ones will work using your solution and which ones do not work depends whether the minimum starting distance between the point and the line segment creates a perpendicular line.
If I can post another picture in the next post, I will put the successful example.
I would have liked to post some code for Sage which produced those images, but the code tags are accepting python unfortunately.
A successful result where the minimum starting distance between the point and the line segment is perpendicular to the line segment:
http://img46.imageshack.us/i/success.png/
Hi the solution I eventually came up with.
Does the ray intersect line segments that are parallel and the specified distance D away from the line segment. Just drawing a rectangle and checking the sides parallel to the line segment.
Does the ray intersect circles of radius D at each end point of the line segment.
Minimize for total unit time to find the first point along the ray that is D away from the line segment.
Possible Border case: Is the start point within D and heads away from the line? Up to the user how to handle this case.
Thanks, that works.
I found the alpha this way:
heading = 45.0*pi/180. #heading 45 degrees.
if x1 > x2: #line segment (x1,y1)<->(x2,y2)
dx = x2 - x1
dy = y2 - y1
else:
dx = x1 - x2
dy = y1 - y2
segmentHeading = atan2(dx, dy)
if heading > 0:
alpha = segmentHeading + heading
else:
alpha = -segmentHeading + heading
t = abs( (dStart - D) / -cos(alpha) ) #-cos in python, sin in C.