My problem is simple.
I am searching a mathematical function to distribute number over an interval.
For example I have this list :
[2; 4; 9; 14]
And in my case I wish
2 -> 1 = f(2)
14 -> 20 = f(14)
4 -> f(4) = ?
9 -> f(9) = ?
This is just an example I am searching for f(x).
Someone would have any idea ?
Thanks for advance ! :)
If you want a linear function, then:
f(x) = lowerFunc + (x - lowerX) * (upperFunc - lowerFunc) / (upperX - lowerX),
where:
lowerFunc: function value at the lower end
upperFunc: function value at the upper end
lowerX: x parameter at the lower end
upperX: x parameter at the upper end.
For your example:
f(x) = 1 + (x - 2) * (20 - 1) / (14 - 2)
= 1 + (x - 2) * 19/12
f(2) = 1
f(4) = 4.1666
f(9) = 12.08333
f(14) = 20
Related
How does spark reduce work for this example?
val num = sc.parallelize(List(1,2,3))
val result = num.reduce((x, y) => x + y)
res: Int = 6
val result = num.reduce((x, y) => x + (y * 10))
res: Int = 321
I understand the 1st result (1 + 2 + 3 = 6). For the 2nd result, I thought the result would be 60 but it's not. Can someone explain?
Step1 : 0 + (1 * 10) = 10
Step2 : 10 + (2 * 10) = 30
Step3 : 30 + (3 * 10) = 60
Update:
As per Spark documentation:
The function should be commutative and associative so that it can be
computed correctly in parallel.
https://spark.apache.org/docs/latest/rdd-programming-guide.html
(2,3) -> 2 + 3 * 10 = 32
(1,(2,3)) -> (1,32) -> 1 + 32 * 10 = 321
A reducer (in general, not just Spark), takes a pair, applies the reduce function and takes the result and applies it again to another element. Until all elements have been applied. The order is implementation specific (or even random if in parallel), but as a rule, it should not affect the end result (commutative and associative).
Check also this https://stackoverflow.com/a/31660532/290036
I have following alghoritm to find line intersection of two planes:
public static function getIntersectOf2Planes ( self $P1 , self $P2 )
{
/* Line equation in parametric form:
x = x0 + t*a
y = y0 + t*b
z = z0 + t*c
*/
$x0 = ( $P1->B * $P2->D - $P2->B * $P1->D ) / ( $P1->A * $P2->B - $P2->A * $P1->B ) ;
$a = ( $P1->B * $P2->C - $P2->B * $P1->C );
$y0 = ( $P2->A * $P1->D - $P1->A * $P2->D ) / ( $P1->A * $P2->B - $P2->A * $P1->B ) ;
$b = ( $P2->A * $P1->C - $P1->A * $P2->C );
$z0 = 0;
$c = ( $P1->A * $P2->B - $P2->A * $P1->B );
$IntersectionLine = new Line3D( $x0, $a, $y0, $b, $z0, $c );
return $IntersectionLine;
}
and it works fine, but to compute $x0 and $y0 i have to divide by:
( $P1->A * $P2->B - $P2->A * $P1->B )
and in some cases, the value of this expression is equal to zero, so I get an "dividing by zero" error :(
What should I do in this case?
I know, that the case when this expression is equal to zero, doesn't mean that there is no intersection, because it's happen when I have planes perpendicular to one of the axies.
For example for:
Plane1:
A = 0
B = 0
C = 100
D = 0
Plane2:
A = 50
B = 0
C = 0
D = -250
so the equation of line should exists.
PS I wrote this code with a view to:
https://math.stackexchange.com/questions/2766615/line-by-two-planes-intersection?noredirect=1#comment5706281_2766615
In short, you have to implement the intersection algorithm for the case when (a1*b2 - a2*b1) = 0 (ie. when the planes are not independent when you set z=0).
To expand on that, first we need to understand how you got this far. First let us write down the equation of two planes:
a1x + b1y + c1z + d1 = 0
and
a2x + b2y + c2z + d2 = 0
When two planes intersect, the intersection is a line. So, the most usual way to solve that is by finding a point first on such a line and then figuring out its orientation (a, b, c) in your case. The orientation is a straight forward cross product. The intersection point is typically calculated by setting one of the co-ordinates to 0 and then solving the 2 linear equations that you get. In your code, this is done by setting:
z = 0
But this only works when the equations
a1x + b1y + d1 = 0 and a2x + b2y + d2 = 0
are capable of giving a solution for x and y, which is not the case when a1b2-a2b1=0. So In such cases, you can solve the same by setting either x or y to 0 which again gives two linear equations that you can solve to obtain a point on the line. Then you can compute the parametric form much like how you did. For example (setting y to 0):
x0 = (c1d2 - c2d1)/(a1c2 - a2c1)
y0 = 0
z0 = (a2d1 - a1d2)/(a1c2 - a2c1)
But for this to be a defined value you need to have (a1c2 - a2c1) to be non-zero. Does this help?
I tried to use erfc but it says argument not optional.
An example is given below
For j = 0 To 150
f = 1
For m = 1 To j
f = f * m
Next
Application.WorksheetFunction.Erf = (Application.WorksheetFunction.Erf) + (-1) ^ j * b ^ (2 * j + 1) / ((2 * j + 1) * f)
Next
Application.WorksheetFunction.ErfC = 1 - 2 / Sqr(3.14) * Application.WorksheetFunction.Erf
MsgBox (Application.WorksheetFunction.ErfC)
xf1 = (wa + 2 * sp) * q / (4 * cl ^ 2 * 3.14 * hf)
xf2 = Exp(b ^ 2) * Application.WorksheetFunction.ErfC
xf3 = 2 * b / Sqr(3.14) - 1
xf = xf1 * (xf2 + xf3)
According to the MSDN documentation at least one parameter needs to be passed to the Erf method:
Name Required/Optional Data Type Description
Arg1 Required Variant Lower_limit - the lower bound for integrating ERF.
Arg2 Optional Variant Upper_limit - the upper bound for integrating ERF.
If omitted, ERF integrates between zero and
lower_limit.
Therefore, calling it with zero parameters (e.g. Application.WorksheetFunction.Erf) will give you an "argument not optional" error.
You also won't be able to set Erf to a value, i.e.
Application.WorksheetFunction.Erf = ...
is invalid.
I'm writing a simple 2D top-down game in Python 3 using tkinter. All the collidable objects are either circles/arcs or lines. I wrote the following method to detect when a circle hits a line:
I am using the formulas y = mx + b and r^2 = (x-h)^2 + (y-k)^2
def CheckHitCToL(self, LX0, LY0, LX1, LY1, CX0, CX1, Tab):
try:
H = self.Creatures[Tab].X
K = self.Creatures[Tab].Y
R = abs((CX0 - CX1) / 2)
M = (LY0 - LY1) / (LX0 - LX1)
B = M * (-LX1) + LY1
QA = (M * M) + 1
QB = (-H - H) + (((B - K) * M) * 2)
QC = (H * H) + ((B - K) * (B - K)) - (R * R)
X = (- QB + sqrt((QB * QB) - (4 * QA * QC))) / (2 * QA)
Y = (M * X) + B
if ((X <= LX0 and X >= LX1) or (X >= LX0 and X <= LX1)) and ((Y <= LY0 and Y >= LY1) or (Y >= LY0 and Y <= LY1)):
return True
else:
return False
except:
return False
My problem is when you have a vertical line, M (Or the slope) is (LY0 - LY1) / 0. (This is because the slope is equal to rise/run, and vertical lines don't have a run, just a rise) Which of course returns an error, caught by try except, which then informs my movement method that no collision has taken place. Of course I can simply move the "try:" down a few lines, but it's still going to throw an error. How can I adapt this program to not throw an error when working with a vertical line?
Well, the most obvious method would involve using if( (LX0 - LX1)==0 ) and doing this case separately. In such cases, you need to check whether distance between LX0 and CX0 is equal to the radius of circle.
You can use another forms of line equation -
implicit A*x + B*y + C = 0
or parametric x = LX0 + t * (LX1 - LX0), y = LY0 + t *(LY1 - LY0)
with appropriate modification of calculations
This is a geometry question.
I have a line between two points A and B and want separate it into k equal parts. I need the coordinates of the points that partition the line between A and B.
Any help is highly appreciated.
Thanks a lot!
You just need a weighted average of A and B.
C(t) = A * (1-t) + B * t
or, in 2-D
Cx = Ax * (1-t) + Bx * t
Cy = Ay * (1-t) + By * t
When t=0, you get A.
When t=1, you get B.
When t=.25, you a point 25% of the way from A to B
etc
So, to divide the line into k equal parts, make a loop and find C, for t=0/k, t=1/k, t=2/k, ... , t=k/k
for(int i=0;i<38;i++)
{
Points[i].x = m_Pos.x * (1 - (i/38.0)) + m_To.x * (i / 38.0);
Points[i].y = m_Pos.y * (1 - (i/38.0)) + m_To.y * (i / 38.0);
if(i == 0 || i == 37 || i == 19) dbg_msg("CLight","(%d)\nPos(%f,%f)\nTo(%f,%f)\nPoint(%f,%f)",i,m_Pos.x,m_Pos.y,m_To.x,m_To.y,Points[i].x,Points[i].y);
}
prints:
[4c7cba40][CLight]: (0)
Pos(3376.000000,1808.000000)
To(3400.851563,1726.714111)
Point(3376.000000,1808.000000)
[4c7cba40][CLight]: (19)
Pos(3376.000000,1808.000000)
To(3400.851563,1726.714111)
Point(3388.425781,1767.357056)
[4c7cba40][CLight]: (37)
Pos(3376.000000,1808.000000)
To(3400.851563,1726.714111)
Point(3400.851563,1726.714111)
which looks fine but then my program doesn't work :D.
but your method works so thanks