### Isometric Projections from Non-square Drawings

Posted:

**Tue Dec 11, 2018 6:43 pm**There might be an easier way to do this in which case I'd be glad to hear it but this is how I did it.

Unless I've overlooked something the isometric projection tool in QCAD only works with drawings that correspond to one of the cardinal directions: plan, front elevation, side elevation or their opposites. I needed to produce isometric views from some drawings of components that fit together at various angles as shown in the attached bitmap.

There is also a tool in in QCAD to produce a projection based on an arbitrary 2x2 matrix and it can be used to produce isometric projections from 2D drawings that are rotated and inclined to the cardinal directions. The attached pdf shows how to calculate the appropriate a, b, c and d values based on rotation and inclination angles.

These values turn out to be:

a = ( cos(R) – sin(R) ) / sqrt(2)

b = - sin(I) * ( cos(R) + sin(R) ) / sqrt(2)

c = ( cos(R) + sin(R) ) / ( sqrt(2) * sqrt(3) )

d = ( sin(I) * cos(R) + 2 * cos(I) - sin(I) * sin(R) ) / ( sqrt(2) * sqrt(3) )

Where R is the rotation angle and I is the inclination.

Perhaps someone else might find this useful or Ribbonsoft might consider another projection tool that takes rotation and inclination parameters.

Unless I've overlooked something the isometric projection tool in QCAD only works with drawings that correspond to one of the cardinal directions: plan, front elevation, side elevation or their opposites. I needed to produce isometric views from some drawings of components that fit together at various angles as shown in the attached bitmap.

There is also a tool in in QCAD to produce a projection based on an arbitrary 2x2 matrix and it can be used to produce isometric projections from 2D drawings that are rotated and inclined to the cardinal directions. The attached pdf shows how to calculate the appropriate a, b, c and d values based on rotation and inclination angles.

These values turn out to be:

a = ( cos(R) – sin(R) ) / sqrt(2)

b = - sin(I) * ( cos(R) + sin(R) ) / sqrt(2)

c = ( cos(R) + sin(R) ) / ( sqrt(2) * sqrt(3) )

d = ( sin(I) * cos(R) + 2 * cos(I) - sin(I) * sin(R) ) / ( sqrt(2) * sqrt(3) )

Where R is the rotation angle and I is the inclination.

Perhaps someone else might find this useful or Ribbonsoft might consider another projection tool that takes rotation and inclination parameters.