Inclined Planes
Another technique we have studied this year is that of drawing inclined planes in perspective, at different angles and on different axes. This is a type of technical perspective drawing that encompasses the rotation of objects in perspective as well as using some techniques from duplication and drawing equidistant objects.
It is possible to rotate cubes in a precise manner in perspective: by drawing a one-point perspective cube and subdividing its lowest side twice, new corner points can be drawn in upon the subdivision corners and joined together. This creates a duplication of the shape slanted at a 45 degree angle. Subdividing this face again will create the points necessary to draw a rotated duplicate at a 22.5 degree angle.
Due to the new rotated shapes being subdivisions of an original, the rotations are constrained by the original planes of the shape. This means that the new rotated shapes are somewhat smaller than the original: as such, if I were to use this technique in future work I would draw the initial shape larger than what I wanted the final rotation to be. This would mean that, when creating a rotation inside the larger initial shape, the rotation would be smaller and therefore the desired size. Alternatively, if I was using a digital medium, I would resize the rotated shape to better fit my composition. I would also use this technique if I was drawing complex shapes at an angle, using the rotated cube as a bounding box to determine where components of the shape would sit, and could also use it as a bounding box if I was drawing characters standing at an angle, whilst within a perspective scene.
There is also a method to drawing slanted planes relative to other shapes in perspective. This is useful when drawing an inclined plane that, though skewed in perspective, is still meant to fit over other planes - such as the lid of an open box. This is a more complex method that uses some techniques from drawing equidistant forms in perspective. To draw a sloped plane in this manner, an initial shape is needed. Against one plane an ellipse is then drawn, with the back vertex as the centre of the ellipse. To draw this shape, the initial plane is equidistantly duplicated horizontally and vertically, creating a series of four planes with the vertex that will be the centre of the ellipse at the middle of them. From this, every plane can be subdivided, showing where the edges of the ellipse should connect.
This ellipse then serves to be the 'hinge' of the plane. Lines can be drawn out to the edges of the ellipse to show where the edge of the slanted plane should sit.
From there, lines can be drawn to perspective points to show how the plane would sit on the shape. These lines may trail to a different vertical point perpendicular to a vanishing point, as the slanted shape sits in a different perspective to the form it is built atop. This technique, though somewhat complicated, would be incredibly useful when drawing open lids and containers, and could also be transferred to drawing adjar doors and open windows, as the panel size is consistent.
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