How can I make a view that seems like orthographic, but not exactly?

Question

For the start, I thought was orthographic, but when I used the orthographic camera, it didn't match up. Client say they want a so-called "industry schematic", talking about a 135 degree look.

I found a trick to do this, which is using lattice. I align the lattice with the cube, and move the upper four points a little bit along the axis showing on the following image. But I want to achieve this by just using the camera.

Answer 1

With some limitations (or I haven't found the how to, probably), we can tweak the camera matrix when using Gpu module. So that we can have the equivalent of viewport rendering.

The image above is taken with a orthographic camera placed in front of some cubes:

On bottom left the addon (see below) shows a vignette of the tweaked image.

When in camera view you can move the camera or the object and view the corresponding result of the projection:

To take a screenshot, use the D key.

Limitations:

• The camera targets along Y and it Y position is fixed to -8 units
• The rendering is limited to the 3D view size
• Moving objects along Y may push them out of the view
• Works in rendered viewport shading but for Eevee or Workbench only (not Cycles)

Principles of the script:

• It is based on simple modal operator template
• Uses this documentation example to make the rendering

The "key" part of the code: as we can give to the GPU module the matrices we want, have added empirical values to make the projection (offset and tweak below).

camera_matrix = scene.camera.matrix_world.copy()
# Static camera position in Y
camera_matrix[1][3] = -8

view_matrix = camera_matrix.inverted()

projection_matrix = scene.camera.calc_matrix_camera(
    context.evaluated_depsgraph_get(), x=width, y=height)

# Empirical offset and perspective tweaks
projection_matrix[0][3] = OFFSET_X
projection_matrix[1][3] = OFFSET_Y

projection_matrix[0][2] = TWEAK_X
projection_matrix[1][2] = TWEAK_Y

# Draw the 3D view    
offscreen.draw_view3d(
    scene,
    context.view_layer,
    context.space_data,
    context.region,
    view_matrix,
    projection_matrix)

Blend file: execute the script then search F3 for "oblique" in the 3D view. Esc to quit. D to take a screenshot. You can zoom in/out by scaling the camera.

The rendering itself is equivalent to "viewport render image" (menu "view"). So you can have the shading you want and disable gizmo and overlays if you want).

Answer 2

Oblique projection Shear matrix to set lattice coordinates

Note: this is adjusting the lattice coordinates based on the shear required, not the camera. IIRC, it has been asked as a feature request to add an Oblique projection to the camera, but AFAIK it isn't available yet.

Without getting into too much theory, I believe this is pretty much shearing the coordinates of the lattice.

For a front ortho projection, it will shear the XZ plane (side walls) along the x, y vector (1, 1) or some multiple of it.

The test code adds a cube with an encompassing default lattice and shears it based on settings for a front view.

EDIT. Oops, I forgot to scale the lattice object, not the data.

How do you freeze or reset a lattice?

import bpy
from mathutils import Matrix, Vector
from bpy import context

shear_dist = 1 # sqrt(2) for (1, 1)
shear_vec = Vector((-1, 1)).normalized()
lattice_res = 8

Sh = Matrix.Shear(
    'XZ',
    4,
    shear_dist * shear_vec,
    )

T = Matrix.Translation((0, 0.5, 0))
def mm(matrix, space=Matrix()):

    return space.inverted() @ matrix @ space

bpy.ops.mesh.primitive_cube_add(
        location=(0, 0, 0),
        )
cube = context.object
bpy.ops.object.add(
        type='LATTICE',
        location=(0, 0, 0))
latob = context.object

latob.dimensions = cube.dimensions
lat = latob.data
lat.points_u = lattice_res
lat.points_v = lattice_res
lat.points_w = lattice_res

latmod = cube.modifiers.new("Oblique", type='LATTICE')
latmod.object = latob

lat.transform(mm(Sh, T))

Ok, I have it better now. The leading face of the cube stays in place.

The next step is to add shape keys for the projections, for example, TOP, LEFT, ... have FRONT.

Answer 3

This is called Oblique projection.
You can't do this in-camera, because Blender doesn't support Oblique camera projection.

You can vote here on Rightclickselect to add Oblique camera projection into Blender.