Hi, I need to be able to calculate the positions of the vertices of a cuboid from the origin given the length of the 3 sides and the angles between the sides.
To define the 3D area
X = 'left to right'
Y = 'front to back'
Z = height.
The origin O is at position (0,0,0).
alpha = angle YOZ
beta = angle XOZ
gamma = YOX
The simple example is a cube. a,b,c = 5 al,be,ga = 90
vertices are (000),(500),(550),(050),(005),(505),(055),(555)
Ok but if i now change the angles beta or gamma the positions of all vertices where x ~= 0 change and if i change alpha all vertices with y~=0 change.
Hope this is example explains what i am after - i need a general route to perform this calculation given any set of angle and any set of different lengths. Effectively this is an attempt to create a unit cell from the a,b,c,al,be,ga parameters,