3. Operations#

This section explains all the operations required to transform the values entered by the user into a camera positioned in 3D space. The user defined values are the alpha & beta angles and the z reduction coefficient for the oblique case. The computed results are the position of the camera in 3D model space expressed by the altitude and rotation angle pair.

Hint

Angle values are displayed in degrees but computed in radians.

3.1. Axonometric Camera#

3.1.1. Input Values#

Attribute	Description	Condition
alpha	The alpha angle of the plan	`alpha + beta > 90°`
beta	The beta angle of the plan	`alpha + beta > 90°`

3.1.2. Math Operations#

#	Variables	Description	Functions
1	alpha, beta	Computes the reduction factors for x, y, and z.	`compute_scales()`
2	alpha, beta, z	Computes the projection altitude	`calculate_axonometric_altitude()`
3	alpha, beta, x, y, z	Computes the projection rotation	`calculate_axonometric_rotation()`
	alpha, beta		`get_tilted_angles()`
			`tilt()`
4	x, y, z	Normalizes the reduction factors for display purposes (informational)	`normalize_factors()`

3.1.3. Output Values#

Attribute	Description
altitude	Computed altitude angle of the camera
rotation	Computed rotation angle of the camera

3.2. Oblique Camera#

Hint

Blender does not natively support oblique projections. To work around this limitation, a small workaround (“hack”) is used.

The camera’s pixel ratio on the X axis is modified in order to stretch the rendered image. This adjustment is computed using the altitude of the projection.

Applied formula: pixel_ratio_x = 1 / sin(abs(altitude))

By combining the camera tilt with this adjusted pixel ratio, it becomes possible to approximate an oblique projection in Blender’s render output.

3.2.1. Input Values#

Attribute	Description	Condition
alpha / beta	The alpha and beta angles of the plane	Their values are linked through the function `calculate_oblique_attributes()`, since `alpha + beta == 90°`
z	The z reduction factor of the plane	`z > 0`

3.2.2. Math Operations#

#	Variables	Description	Functions
1	z	Computes the projection altitude using the z reduction factor	`calculate_altitude_with_z_value()`
2	beta	Deduces the projection rotation from the beta angle (beta = rotation)

3.2.3. Output Values#

Attribute	Description
altitude	Computed altitude angle of the camera
rotation	Computed rotation angle of the camera