Graph with logarythimic y axis in Swift - swift

My goal is to create a graph similar to a picture below. I actually managed to implement it with combination of a magic numbers and set scale (0.001 - 1000). So to summarize I am looking for a formula that will calculate right position to plot lines on logarithmic y scale for range of predefined values.
Y axis: logarithmic scale
X axis: Integers
Any help will be welcome!

I solved it thanks to help of #DietrichEpp. Here is the function that calculates Y coordinates given:
screenY0 - min point on y axis
screenY1 - max point on y axis
dataY0 - value responding to the top of the scale
dataY1 - value responding to the bottom of the scale
func convert(data: Double, screenY0:CGFloat, screenY1:CGFloat, dataY0:Double, dataY1:CGFloat) ->CGFloat{
return screenY0 + (log(CGFloat(data)) - log(CGFloat(dataY0))) / (log(CGFloat(dataY1)) - log(CGFloat(dataY0))) * (screenY1 - screenY0)
}

Related

Recalculate values on different scale in chart

I want to display some values inside a chart-like tool based on pixels.
Problem is that the left xAxis has a max scale of 200 pixel. Inside that pixel square i want to display different altitude values that can range from 200m-1500m or 324m-724m or anything else.
So i need to recalculate the orignal values by a factor to display them inside this chart. Haven't find the right solution yet. Any hints ?
You have range of Y-coordinates 0..YMax (200 for your case) and data range Data_Low..Data_High (find min and max values).
To map data range to axis range, use linear formula:
Y = (Value - Data_Low) * YMax / (Data_High - Data_Low)
If axis starts from YMin, use
Y = YMin + (Value - Data_Low) * (YMax - YMin) / (Data_High - Data_Low)

Calculating a spiral in MATLAB

We have these logarithmic spirals which are circling around the centre of the coordinate system:
x = ebθ cos(θ)
y = ebθ sin(θ)
where the ebθ is the distance between the point (which is on the spiral) and the centre; and the θ is the angle between the line connecting the point and the origin and the axis x.
Consider a spiral where the angle is θ ϵ <0,10π> and the parameter is b=0.1. By thickening points on the spirals (and the angle θ) calculate the circumference with the relative precision better than 1%. Draw the spiral!
I'm preparing for a (MATLAB) test and I'm stuck with this exercise. Please help, any hint is appreciated.
Start by computing a list of x,y for your range of theta and value of b. For more accurate results, have your theta increment in smaller steps (I chose 5000 arbitrarily). Then, its simply computing the distance for each pair of consecutive points and summing them up.
t = linspace(0,10*pi,5000);
b = 0.1;
x = exp(b*t).*cos(t);
y = exp(b*t).*sin(t);
result = sum(sqrt((x(2:end) - x(1:end-1)).^2 + (y(2:end)-y(1:end-1)).^2))

Ellipse - Finding the y-coordinate for a specific x co-ordinate

I was wondering if anyone can help me. I'm trying to modal an oval room, and the joists run parallel to one another at 400mm intervals, starting and finishing 200mm from the apexes of the oval. The central joist falls on the centre of the oval at (0,0).
So the oval is positioned at angle = 0, with a centre of (0,0). The major axis is 6000mm long in the x-direction and the minor axis is 3500mm long in the y-direction. The joists run in the y-direction too.
I need to find out the node for each joist along the outside edge of the ellipse. So obviously, I know the x values will be -2800, -2400, ..., 0, ..., 2000, 2400, 2800, and that the central joist will have one node at (0, 1750) and one at (0, -1750), but how can I find the y values for all the other x co-ordinates?
Many thanks.
p.s. In case you can't tell I have exceedinly rudimentary MATLAB skills.
It's convenient to work with semi-axes, denoted a and b below. The equation of ellipse is (x/a)^2+(y/b)^2=1, which gives two values of y, positive b*sqrt(1-(x./a)^2) and negative b*sqrt(1-(x./a)^2).
In MATLAB you can compute them this way:
a = 6000/2;
b = 3500/2;
x = -2800:400:2800;
yP = b.*sqrt(1-(x./a).^2);
yN = - yP;
So, yP contains the positive y-coordinates and yN contains negative y-coordinates.
The dots in front of arithmetic operations mean they are performed on vectors componentwise.

Dome rotation on arbitrary axis?

Imagine a dome with its centre in the +z direction. What I want to do is to move that dome's centre to a different axis (e.g. 20 degrees x axis, 20 degrees y axis, 20 degrees z axis). How can I do that ? Any hint/tip helps.
Add more info:
I've been dabbling with rotation matrices in wiki for a while. The problem is, it is not a commutative operation. RxRyRz is not same as RzRyRx. So based on the way I multiple it I get a different final results. For example, I want my final projection to have 20 degrees from the original X axis, 20 degrees from original Y axis and 20 degrees from original Z axis. Based on the matrix, giving alpha, beta, gamma values 20 (or its corresponding radian) does NOT result the intended rotation. Am I missing something? Is there a matrix that I can just put the intended angles and get it at the end ?
Using a rotation matrix is an easy way to rotate a collection of (x,y,z) points. You can calculate a rotation matrix for your case using the equations in the general rotation section. Note that figuring out the angle values to plug into those equations can be tricky. Think of it as rotating about one axis at a time and remember that the order of your rotations (order of multiplications) does matter.
An alternative to the general rotation equations is to calculate a rotation matrix from axis and angle. It may be easier for you to define correct parameters with this method.
Update: After perusing Wikipedia, I found a simple way to calculate rotation axis and angle between two vectors. Just fill in your starting and ending vectors for a and b here:
a = [0.0 0.0 1.0];
b = [0.5 0.5 0.0];
vectorMag = #(x) sqrt(sum(x.^2));
rotAngle = acos(dot(a,b) / (vectorMag(a) * vectorMag(b)))
rotAxis = cross(a,b)
rotAxis =
-0.5 0.5 0
rotAngle =
1.5708

core-plot iOS reversed Y axis

I would like to use core-plot to display a water depth graph (updated in real time) but I can't figure out how to reverse the Y axis, so that the X axis (representing the time domain) is on the top of my UIView and the Y axis grows towards the bottom with positive values.
EDIT
It would be even better if I could draw axes like this:
- X axis is time
- Y axis is from 0 to X (X > 0) and on the top there is 0, on the bottom there is X
- X axis is on the bottom
ASCII version:
0 |
1 |
.
.
.
x |
--------------------------
0 1 2 3 4 5 6 7 ...
You can use a negative length for the plot range to reverse the direction of an axis. For example (from the axis demo in CPTTestApp):
plotSpace.xRange = [CPTPlotRange plotRangeWithLocation:CPTDecimalFromDouble(0.0)
length:CPTDecimalFromDouble(-10.0)];
This ended up being a bit tricky to understand from the accepted answer. To add another example for anyone having issues understanding how to flip the y axis values in coreplot, you really need to declare the plotRangeWithLocation to be the positive number you want to achieve, then set the length to the same negative number like this:
plotSpacePressureLeft.yRange = [CPTPlotRange plotRangeWithLocation:CPTDecimalFromFloat(9000)
length:CPTDecimalFromFloat(-9000)];
This produces a y-axis like this as of iOS 14 and coreplot mid 2020 versions: