Whirling Ribbons

Returns an x,y,z pair rotated on the XY plane L: an x,y,z pair as a list of length 3 θ: angle of rotation

Returns an x,y,z pair rotated on the XZ plane L: an x,y,z pair as a list of length 3 θ: angle of rotation

Returns a x,y,z pair rotated on the YZ plane L: an x,y,z pair as a list of length 3 θ: angle of rotation

Returns a pair of x,y,z after rotated to the current view angle for projection

Returns the x of the rotated x,y,z for projection

Returns the y of the rotated x,y,z for projection

Returns the z of the rotated x,y,z for projection

Projects an x,y,z pair with the current view angle

Projects an x,y,z pair with the current view angle P_1: an x,y,z pair as a list of length 3

Returns the angle (0<=θ<=360, or 2π) between two points, P1 & P2

Returns the angle (0<=θ<=360, or 2π) between a 2D point & the initial side of the x-axis

Returns the linear interpolation between two points. Returns P1 when t = 0, returns P2 when t = 1.

Graphs a line between two points x1, y1, z1: x,y,z of the first point x2, y2, z2: x,y,z of the second point t: from 0 to 1

Graphs a line between two points P_1: an x,y,z pair as a list of length 3 P_2: an x,y,z pair as a list of length 3 t: from 0 to 1

Returns an x,y,z pair after applied quaternion rotation. V (vx,vy,vz) is the axis of rotation. The distance of V from the origin must be 1. A is the angle of rotation. x,y,z is the 3D point rotated. (Ideally, this function should be written in quaterion algebra if Desmos allows. I used Matlab to expand the quaternion algebra into normal algebra.)

Learn quaternions: https://www.3dgep.com/understanding-quaternions/ https://www.youtube.com/watch?v=d4EgbgTm0Bg (3Blue1Brown) https://youtube.com/watch?v=zjMuIxRvygQ (3Blue1Brown)

Returns an x,y,z pair after applied quaternion rotation. V (vx,vy,vz) is the axis of rotation. The distance of V from the origin does not have to be 1. A is the angle of rotation. x,y,z is the 3D point rotated.

Same as the function above, except vx,vy,vz and x,y,z are taken as a list.

Returns a point on a sphere of radius 1 with the given latitude & longitude (https://bit.ly/3mubei9). λ: Longitude, or the left & right on a sphere ϕ: Latitude, or the up & down on a sphere

Returns the distance of a point from the origin

Returns the distance between two points

Returns the dot product of a point

Returns the difference in angle between two points using dot product

Returns the vector length of the cross product of two 2D points

Returns the cross product of two 3D points

Returns an x,y,z pair rotated to a certain normal L is the x,y,z pair rotated V is normal that L is rotated to. The distance of V from the origin does not have to be 1.

Same as the meshgrid method in Matlab & python: returns all permutations between two 1D arrays as a 1D array; useful for generating 2D arrays stored as 1D array.