CODEWITHSUNDEEP
javascriptpythonmathgeometry
Thomas Turner
Thomas Turner

Reputation: 3042

Finding a point along an arc

I am trying to write a Python or JavaScript routine that finds two point on an arc.

I will go in to the routine with a start_distance and end_distance. I want to move around the circumference of arc a given amount and then return the new x's and y's. In affect I am trying to move the start and end points of my arc.

My input to the routine will be

def get_points_on_an_arc(x1, y1, x2, y2, radius, large, clockwise, start_distance, end_distance)
     # logic here
     return s_x, s_y, e_x, e_y

Here is a image that might help you.

enter image description here

Any idea on how to write this?

Thanks

Upvotes: 3

Views: 1661

Answers (3)

Song
Song

Reputation: 328

solution

I have written this code:

the code

class Circle:
    def __init__(self, rds):
        '''rds:radius    delete:ctr:center   of circle'''
        self.rds = rds

    def isoncircle(self, point):
        '''a check if point is on circle'''
        if point_on_circle:
            return True
        return False

    def get_point(self, start=[0, 0], distance=2, direction='c'):
        '''start:bottom point   distance:distance to move up or down    direction:move up or down'''
        if direction == 'c':
            cme = [start[0]+abs(distance-self.rds), start[1]+abs(distance-self.rds)]
        elif direction == 'cou':
            start = [start[0], start[1]-(self.rds*2)]
            cme = [start[0]-abs(distance-self.rds), start[1]-abs(distance-self.rds)]
        if self.isoncircle(cme):
            return cme

    def get_points(self, sd, ed):
        s_x, s_y = self.get_point(distance=sd, direction='c')
        e_x, e_y = self.get_point(distance=ed, direction='cou')
        return s_x, s_y, e_x, e_y

circle = Circle(4)
circle.get_points(4, 4)

Class Functions

The init function does all the setting up.

The isoncircle function checks if a point is on the circle.

The get_point function gets an end point.

The get_points function sums it all up and gets the two end points.

Summary

Take a careful look and you can change the distances and even the start point in the get_point function.

If any of this is unclear, let me know.

Upvotes: 0

tenfishsticks
tenfishsticks

Reputation: 452

class Circle(object):
    def __init__(self, center=(0,0), radius=1):
         """ Center and radius define a unique circle """
         self._center = center
         self._radius = radius
    ...

    def isOn(self, point):
        if point_on_circle:
            return True
        return False
    ...

    def get_new_point(self, start=(1,0), distance=1, direction='clockwise'):
        """ Inputs:
          circle - instance of the Circle() class
          start  - tuple of (x, y) the exists on circle
          distance - distance to travel in radians
          direction - 'clockwise' or 'widdershins'
        """
        assert circle.isOn(start), "Start point is NOT on the circle"
        # code to calculate new point here - basic geometry, use Google
        end = ...
        return end

    def get_points_on_an_arc(self, x1, y1, x2, y2, large, clockwise, start_distance, end_distance):
        """ Your function signature will ONLY work if it is a class method 
            The alternative is to change the signature and explicitly pass in a Circle() object to the function
        """
        s_x, s_y = get_new_point(start=(x1, y1), distance=start_distance, direction='clockwise')
        e_x, e_y = get_new_point(start=(x2, y2), distance=end_distance, direction='widdershins')
        return s_x, s_y, e_x, e_y

Upvotes: 0

MBo
MBo

Reputation: 80187

At first you need to find circle center. It lies on middle perpendicular to P1-P2 segment. Middle point. 

M = (P1 + P2)/2  
P12 = P2-P1 = (P12.X, P12.Y)

Perpendicular to P12 vector is 

PP = (-P12.Y, P12.X)

Center
C = M + PP * t where t is parameter.
you need to solve equation 

(C-P1)^2 = R^2

against t parameter, then choose one of two possible solutions to fulfill requirements (large, clockwise)
(for example, through sign of scalar product of CP1 and CP2)

When center is found, the rest of problem is easy: rotate P1 by (StartDistance/R) angle around the center, and rotate P2 by (-EndDistance/R) angle.

Upvotes: 2

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