Normal calculation for Splines [closed] - math

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I would like to implement a revolve tool for 2d splines in 3d. The geometry computation already works but the normals are a bit tricky.
The problem is the angle between 2 points like the following image:
Here P1 is the previous point P2 the current point and P3 the next point.
How would I calculate the vector N.

Are you looking for the inverse angle bisector?
dir1 = normalize(p1 - p2)
dir2 = normalize(p3 - p2)
n = normalize(-dir1 - dir2)

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Why does the desnity plots exceed the unity value in the hist(x,freq="FALSE") command of R? [closed]

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I am using hist(x_new,freq = FALSE) command to plot histogram, but the probability density exceed the value unity.
Probability density is not the same thing as probability. Densities are not in general bounded by 1. The point is that the total area under the density is 1, which is completely consistent with portions of it being above 1. In fact, it is quite common for a density function (or density histogram) to be above 1 in some places.

is there a way to sort GPS data by vehicle ID in R so that I can extract the starting point for all the vehicles [closed]

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I have passive GPS data(approx 500000 spatial points) for around 10,000 vehicles.I need to find the first point for each of the vehicles.Each spatial point is associated with its own id.I need to get the first point from each id.
If your data.frame is called data1 and columns are vehicleID, x, y, etc.
data1[order(data1$vehicleID),]
If you want to just return the first point of each vehicle.
data1[data1$vehicleID==1,]

How to draw a decision tree in R [closed]

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I want to present (draw) a flow of decisions starting from root continue decision nodes up to 6 layers.
The decision root (R) will splits into 2 decision options X1 and X2, each of these Xs then divided into 3 new branches of Y1, Y2, and Y3,
then Ys divided into 3 branches Z1, Z2, and Z3, and so on.
Please note that I am not going to classify or doing recursive analysis.
Any help please?
You could use rpart.plot package in R which is used to plot Classification and Regression Trees. One such example is
This link would be helpful for examples.

Plotting Location data in R [closed]

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Can anyone please tell me how to plot location data in the R language?
Suppose I have data "Date-time" with X and Y coordinates (latitude and Longitude) as mentioned below;I am trying to do in R language.
Date: 2016-02-25 17:21:09.147,
Location (2.39, 48.71)
To visualise your 3D data, you can use plot3d and combine it with datetick to format the time axes.

Vector2 intersection [closed]

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I'm developing a little 2D game and i have to predict when and where things will collide.
So, i've got four Vector2 :
A position
B position
A linear velocity
B linear velocity
I have to find if they intersect, where they intersect and at what time from now.
I've found many math solutions but i could't translate them into code.
The visualization of the problem, numbers are velocities
You want to compute the minimum of
norm((A+t*vA)-(B+t*vB))=norm((A-B)+t*(vA-vB))
Taking the square of these Euclidean norms
norm((A-B)+t*(vA-vB))^2 = norm(A-B)^2 + 2*t*dot(A-B,vA-vB) + t^2*norm(vA-vB)^2
gives you a simple quadratic function in t where the minimum has the value
min_dist =norm(A-B)^2 - dot(A-B,vA-vB)^2/norm(vA-vB)^2
at time
t = -dot(A-B,vA-vB)/norm(vA-vB)^2

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