Example: if the cursor is at then we determine that it's over Cell_1_1 and Active_Cell = Cell_1_1. Using the coordinates of an active cursor we can calculate which cell the cursor is over (some Cell_p_q) and designate that cell the Active_Cell which is then highlighted. Cell_p_q), and an active cursor (denoted by its rendered position ) In other words, World_A has a 2-dimensional, 4096 x 4096 pixel map with an initial orientation of -90 degrees (inverse Cartesian plane), which can be divided by 64 x 64 named cells (denoted by their calculated subcoordinates e.g. Now assume we have a World instance called World_A with the following properties: See graphic on bottom.Īssume a game world has four properties World => ( ORIENTATION = angle, MAP_SIZE =, CELL_SIZE = ) I need to understand the math for this (some pseudo code might be helpful). The bond vector definition is here: def get_bond_vector(r, a, t):Īgain, the only part I don't understand is # get local axis system from 3 coordinates.Apologies if my example is a bit contrived, I've been trying to figure out how to apply matrix transformations to this coordinate problem, and I'm not getting the right output. Here is some context of how this function is used: bond_vector = get_bond_vector(atom.rval, atom.aval, al)ĭisp_vector = np.array(np.dot(bond_vector, _axes))Ītom.coords = + disp_vector What is "getting local axis system from 3 coordinates"? U23c21 = get_ucp(u23, u21) # unit cross product Print('\nError: Co-linear atoms in an internal coordinate definition') U23 = get_u12(coords2, coords3) #calculating vector between that points 2-3 U21 = get_u12(coords1, coords2) #calculating vector between that points 1-2 However, in his work, there is a mathematical part that I don't understand: # get local axis system from 3 coordinatesĭef get_local_axes(coords1, coords2, coords3): While searching I found TMPChem's work on GitHub and it does exactly what I want. If there aren't any mistakes up to this point, how I will calculate Cartesian coordinates of the 4th atom using these $x,y,z$ values? To calculate $x,y,z$ values from the formulas x = r * sin(theta) * cos(phi) I am not sure if I should calculate this as z2 + s(angle) or z2 - s(angle) and what it depends on, if both are possible.įor the 4th atom, I use spherical coordinates r, theta, phi = (0.976, 96.572, -179.995) The 3rd atom must have coordinates that are something like this if read correctly: 3 H 0 distance*sin(angle) z2+distance*cos(angle) How should I treat the 3rd and 4th atoms? My question is after setting first atom as 0,0,0 1 O 0 0 0Īnd the second one as 0,0,(distance from first) to put it on the z-axis 2 O 0 0 1.45335189476 This is converting a Z-matrix to Cartesian coordinates. Now I need to perform the reverse operation and use this Z-matrix as input and define $x,y,z$ coordinates for each atom. Then, the script constructs a Z-matrix with them, like this: Z-mat : These are $x,y,z$ coordinates of H2O2 molecule. To begin with, I wrote a script that gets Cartesian coordinates of molecule as input in the below.
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