Circles of given radius through two points: Difference between revisions
Circles of given radius through two points (view source)
Revision as of 16:03, 12 November 2018
, 5 years ago→{{header|Maple}}
m (→{{header|C}}) |
|||
Line 1,687:
It will be a single point (0.1234,0.9876) of radius 0
</lang>
=={{header|Lua}}==
{{trans|C}}
<lang lua>function distance(p1, p2)
local dx = (p1.x-p2.x)
local dy = (p1.y-p2.y)
return math.sqrt(dx*dx + dy*dy)
end
function findCircles(p1, p2, radius)
local seperation = distance(p1, p2)
if seperation == 0.0 then
if radius == 0.0 then
print("No circles can be drawn through ("..p1.x..", "..p1.y..")")
else
print("Infinitely many circles can be drawn through ("..p1.x..", "..p1.y..")")
end
elseif seperation == 2*radius then
local cx = (p1.x+p2.x)/2
local cy = (p1.y+p2.y)/2
print("Given points are opposite ends of a diameter of the circle with center ("..cx..", "..cy..") and radius "..radius)
elseif seperation > 2*radius then
print("Given points are further away from each other than a diameter of a circle with radius "..radius)
else
local mirrorDistance = math.sqrt(math.pow(radius,2) - math.pow(seperation/2,2))
local dx = p2.x - p1.x
local dy = p1.y - p2.y
local ax = (p1.x + p2.x) / 2
local ay = (p1.y + p2.y) / 2
local mx = mirrorDistance * dx / seperation
local my = mirrorDistance * dy / seperation
c1 = {x=ax+my, y=ay+mx}
c2 = {x=ax-my, y=ay-mx}
print("Two circles are possible.")
print("Circle C1 with center ("..c1.x..", "..c1.y.."), radius "..radius)
print("Circle C2 with center ("..c2.x..", "..c2.y.."), radius "..radius)
end
print()
end
cases = {
{x=0.1234, y=0.9876}, {x=0.8765, y=0.2345},
{x=0.0000, y=2.0000}, {x=0.0000, y=0.0000},
{x=0.1234, y=0.9876}, {x=0.1234, y=0.9876},
{x=0.1234, y=0.9876}, {x=0.8765, y=0.2345},
{x=0.1234, y=0.9876}, {x=0.1234, y=0.9876}
}
radii = { 2.0, 1.0, 2.0, 0.5, 0.0 }
for i=1, #radii do
print("Case "..i)
findCircles(cases[i*2-1], cases[i*2], radii[i])
end</lang>
{{out}}
<pre>Case 1
Two circles are possible.
Circle C1 with center (1.8631118016582, 1.9742118016582), radius 2
Circle C2 with center (-0.86321180165819, -0.75211180165819), radius 2
Case 2
Given points are opposite ends of a diameter of the circle with center (0, 1) and radius 1
Case 3
Infinitely many circles can be drawn through (0.1234, 0.9876)
Case 4
Given points are further away from each other than a diameter of a circle with radius 0.5
Case 5
No circles can be drawn through (0.1234, 0.9876)</pre>
=={{header|Maple}}==
| |||