Axonometric and perspective representation for design
Axonometric and conical representation questions check that you can build a believable three-dimensional image with the correct axes, reduction coefficients and vanishing geometry. In the PAU the most frequent items are an isometric view of a piece with cylindrical holes, a caballera projection, and a conical perspective of a simple volume.
Core rules
- Axonometric system: the three axes and their reduction coefficients come from the triángulo de trazas. Isometric: axes 120° apart (30° to the horizontal), natural reduction 0.816; the isometric drawing uses full scale along the axes, which is equivalent to enlarging by 1.22.
- Caballera: the frontal face keeps its true shape; the y-axis is drawn at 45° (or 30°/60°) with a reduction of 0.5 (perspectiva caballera), giving the familiar depth compression.
- Circles in axonometry become ellipses: in isometric drawing the major axis is 1.22d and the minor 0.71d, with the major axis perpendicular to the axis that is normal to the plane of the circle.
- Conical perspective: plano del cuadro, línea de tierra, línea de horizonte, punto principal and distancia principal (equal to the height of the point of view). Lines parallel to the picture plane keep their direction; all others converge on a punto de fuga. Heights are transferred with the ground line and the horizon, or with a scale on the picture plane; distances along a line use its punto métrico.
- Distortion control: the visual cone is about 60°, so the distance from the observer to the picture should be at least 1.7 times the diagonal of the framed area.
Worked example
Isometric drawing of a 30 mm cube with a ⌀30 circle centred on the top face. Draw the three axes at 30° to the horizontal, mark all edges at 30 mm (no 0.816 factor, this is an isometric drawing), then draw the ellipse on the top face with major axis 1.22 × 30 = 36.6 mm, perpendicular to the vertical axis, and minor axis 0.71 × 30 = 21.3 mm. The same ellipse repeats on the two vertical faces, each rotated to stay perpendicular to the remaining axis.
Traps that cost marks
Drawing isometric axes at 45°; applying the 0.816 reduction while measuring true lengths on the axes; aligning the ellipse's major axis with the face axis instead of perpendicular to it; forgetting the 0.5 reduction on the caballera depth; mixing the horizon and ground lines; measuring heights directly on the horizon instead of transferring them with the ground line.