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Aspect distortion of relative vectors composed in NDC space

The distortion affects relative vectors calculated in NDC (OpenGL Normalised Device Coordinates) space at the point at which they are mapped to a rectangular (i.e. non-square) screen.

Let the metric used to measure distance be the proportion of the height of the (NDC cube)/screen. Let's say we wish to calculate a position Q in NDC which is a desired distance from P on the screen.

fospathi

Create a new GitLab project from an existing local repository

This SSH method assumes your SSH keys are already set up on Gitlab and your local system. The SSH method is preferable as it doesn't require a username and password like the HTTPS method.

In the commands below replace fospathi and nonexistent-project with your username and project name respectively. Execute these commands in the project's top-level directory which usually contains the project's .git directory and other language specific things like a go.mod file for Go modules.

Git push using SSH

Directly push the repo to GitLab to create the new project (some times this step takes multiple attempts before success):

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⚠️ This discussion applies to version 1.13 (released 2019) of the Go language.

Why are Go's identical errors not equal?

Or, more precisely, why are two separate but otherwise seemingly identical errors created by Go's errors.New function not equal according to the == operator?

Consider the output of the following small program (Go Playground link) which compares Go's error values for equality:

package main

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An expression for the launch angle of a parabolic projectile which coincides with a target position vector (x, y) at some 
point in its trajectory.

The parametric coordinates of a parabolic projectile launched from the origin are
  
    x = uct
    
    y = ust + at² / 2
    
where 

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An expression for the sin curve's principal unit normal vector.

The principal unit normal vector is different from a unit normal vector in that it always points from a point on the curve
towards the centre of the circle that most closely approximates the curvature of the curve at that point. Thus, the principal
unit normal vector is undefined at inflection points since the radius of the circle is infinite at these points.

Consider the parametric form of a sin curve. Let R be a general position vector on a sin curve and let 

c = cos(t)
s = sin(t)

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Let the vector v be a function of time and k be a constant vector. Find the time derivatives of 

1. |v|^2

   d |v|^2 = d  (v⋅v)
   dt        dt
           = dv⋅v + v⋅dv
             dt       dt
           = 2v⋅dv
                dt

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Affine transformation matrices to reflect a point in (1) the XY-plane through the origin; (2) an arbitrary 3D plane. 
A right-handed coordinate system is assumed.

1. XY plane at z=0

Consider a reflection in an XY-plane located at the origin. To accomplish this we require a matrix M such that

  |x|   | x|
M |y| = | y|
  |z|   |-z|

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Affine transformation matrices to rotate around (1) the X-axis; (2) the Y-axis; (3) the Z-axis; (4) an arbitrary 3D line. A 
right-handed coordinate system is assumed.

1. X-axis

Z-axis |           'B                A and B are two points in a YZ-plane
       |         '                   ∠ AOB = β
       |       '       `A            ∠ YOA = α
       |     '     `                 |OA| = |OB| = r
       |   '   `   

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Let L₀ = P₀ + αD₀ and L₁ = P₁ + βD₁ be two lines. Let P = P₁ - P₀ and 

L = L₁ - L₀
  = P - αD₀ + βD₁

Then 

L²  = L⋅L
    = (P - αD₀ + βD₁)⋅(P - αD₀ + βD₁)
    = P² + (αD₀)² + (βD₁)² - 2α(P⋅D₀) + 2β(P⋅D₁) - 2αβ(D₀⋅D₁)

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The Y-axis in an SVG document points towards the bottom of the page, that is the Y value increases the further down the page 
you go. When positioning items in a maths or physics context however it is more appropriate to have the Y-axis pointing up 
the page like a normal coordinate system. We can provide an affine transformation matrix to a g element's transform 
attribute that flips the Y-axis for its children.

Let the value of the viewBox attribute of the document's SVG element equal "0 0 w h". Suppose we want a coordinate system
whose origin is at the centre of the viewbox and whose Y-axis points up to the top of the page.
 
    (0, 0)
       O_ _ _ _ _ _ _ _\ X  (Default SVG coordinate system/frame)