Movement on the orthogonal plane

This mode of position editing is particularly complex and rarely used, but it offers even greater control over movement. While the traditional mode uses the axes and therefore the real planes relative to the workspace as a reference, here we use mutable references, the inclusion of which leads to results that are not entirely predictable, since the primary reference is our POV.

We spoke earlier of a Cartesian system in relation to the management of the POV. We can therefore say that, in this system, the three axes x, y and z (locked) correspond to the axes of tilting, panning and rolling (locked) already mentioned.

This mode is activated by selecting the position instrument and pressing the SHIFT button and holding it down during operations

As you can see from the images, only two axes are shown, describing a plane on the object that is orthogonal to our POV. In fact, movement is allowed along the tilting and panning axes and on the plane they describe.

In fact, we have to imagine that the rolling axis is a straight line, perpendicular and anchored to us, and that this new Cartesian system always remains fixed relative to our POV and therefore variable with respect to space.

In whatever direction we point the POV, these two axes and the square at their intersection remain fixed. And here is the complexity: the coordinates displayed in the control mirror always represent the real spatial coordinates of the object, but when we act on the arrow representing the tilting axis (the orthogonal x-axis according to the POV), the object will move in a direction that is concordant with the axis and our POV, but relative to space it will move instead on the real x and z.

Since rotation cannot be applied to the rolling axis, the movement applied to the tilting axis (a horizontal directional axis) will always be parallel to the real horizontal plane.

Note: in this mode the snap is active, but it moves per unit. Each step will therefore measure 1m.

An example will better explain the concept:

Let us empirically set up a POV by placing the space in a perspective as balanced as possible, with a rotation corresponding to about 45° on all axes. We will realize the success of this operation by observing the three intersecting planes of the axes: the union of the three squares, prospectively three rhombuses, will draw a regular hexagon. In this particular case, however, the greater precision sought is not so much in the angle with respect to the y axis, but in the balance between the real x and z axes.

By setting with the SHIFT key to orthogonal mode, the tilting axis is in a position that suggests an equal shifting in the real plane relative to the x and z coordinates, that is, a shifting of the object on a diagonal between the two axes.

We therefore apply a translation of the object on this relative axis by moving to the right. It has already been mentioned that the shifting is by unity, that is 1m from the starting point. We have therefore ideally moved the object 1m along the hypotenuse of a triangle described by an increment of x and an equal increment of z.

The Pythagorean theorem and a quick calculation will then tell us that the displacement on the real axes was incremental by a value of 0.7. The start coordinates [x: 24 y: 0 z: -24] and the end coordinates [x: 24.7 y: 0 z: -23.3] confirm the correctness of these calculations.

If this is true, what is expected from an action on the panning axis (the y of the POV)?

Again, the answer can be complex, because if a rotation on the panning axis can affect the angular direction involving the real x and z through a translation on the tilting axis, a rotation on the tilting axis will also change the angle of incidence on the real plane: a translation on the panning axis (a vertical directional axis) will then affect all directions, affecting x and z of the object according to the direction indicated by the arrow, and y according to the tilting angle.

The following is a practical example of a combined translation on the tilting and panning axes of a fixed POV.

The translation just illustrated was carried out quickly by moving the small square at the intersection of the axes: moving it to the right and upwards resulted in an incremental translation involving x, y and z. In fact, it can be seen that although the step is unity, the y reports a final value of 0.8, determined by the particular angle of the tilting axis.

But does the panning axis really force vertical translation?

Short answer: no.

To say that rolling is not enabled is to say that it is fixed at a rotation angle of 0°.

But tilting is possible over an angle of 360°. This means that a POV that is perfectly orthogonal to the plane, i.e. with a rotation on tilting for an angle of 90°, will cause the panning axis to be parallel to the plane itself.

In this state, the tilting axis and the panning axis will both affect x and z depending on the direction.

The translated object then retains its y value.

In the following example, the movement of the yellow cube resting on the plane keeps the y: 0 value constant.