python - 2 math questions

问题:

Hey, I'm using pyGame and I want to:

A) make a function that returns the angle between two points. I've tried doing this with math.atan2 and I'm getting really wierd returns. I tried this with both (delta X, deltaY) and (deltaY, deltaX). Any suggestions?

B) given a length and an angle, return a point using those two from 0. For example, LengthDir(2,45) using (length,angle) would return (2,2).

Thanks for the help. I've searched all over the internet and I couldn't find anything to help me...

回答1:

math.atan2 returns radians. If you need degree, multiply the result by 180/π.

def A(dx, dy):
  return math.atan2(dy, dx) * 180 / math.pi

Similarly, all trigonometric functions in math operate in radians. If you input a degree, you need to multiply by π/180 first.

def LengthDir(length, angle):
  radian_angle = angle * math.pi / 180
  return (length * math.cos(radian_angle), length * math.sin(radian_angle))

Python provides the convenient functions math.degrees and math.radians so you don't need to memorize the constant 180/π.

def A(dx, dy):
  return math.degrees( math.atan2(dy, dx) )

def LengthDir(length, angle):
  radian_angle = math.radians(angle)
  return (length * math.cos(radian_angle), length * math.sin(radian_angle))

回答2:

You could use the functions in cmath to convert between rectangular and polar coordinates. For example:

import math, cmath

def LengthDir(r, phi):
   c = cmath.rect(r, math.radians(phi))
   return (c.real, c.imag)

def AngleBetween((x1, y1), (x2, y2)):
   phi = cmath.phase(x2 + y2*j) - cmath.phase(x1 + y1*j)
   return math.degrees(phi) % 360

回答3:

import math

def dist(dx,dy):
    return math.sqrt(dx*dx + dy*dy)

def ang(dx, dy):
    return math.degrees(math.atan2(dy, dx))

def offs(dist, ang):
    ang = math.radians(ang)
    dx = dist * math.cos(ang)
    dy = dist * math.sin(ang)
    return dx,dy

.

dist(2,2) -> 2.8284
ang(2,2) -> 45.0
offs(2, 45) -> (1.414, 1.414)