两点透视学习笔记

两点透视的整体主题是，通过将消失点旋转特定角度以及在合适的measure bar上确定相应的measure points以便投射所需的深度等办法，确定物体在两点透视中的正确比例。

定位测量点（locating the measure points）

在一点透视中，单个消失点（principal point）决定了空间中沿着纵深线（指向principal point的消失线）方向上的透视变化，而对角消失点则可以将测量单位从图像平面投射到纵深线上。

在两点透视中，principal point仍然定义了观察者的纵深方向的透视变化，以及direction of view在地平面和所有平行于视线方向的平面上产生的透视梯度。但物体本身的消失点却在两个不同的方向上发生着各自的透视变化（即两条消失线），我们的任务便是沿着这些消失线建立测量单位。

Geometry of Measure Points. In the context of the visual ray method of perspective construction, the problem is to project a distance scale or unit dimension, defined along the ground line, into perpspective space along a vanishing line to one of the object vanishing points.

定位测量点其实超级简单，只需draw an arc from each vanishing point, from the viewpoint to the horizon line (image plane)

who has a 12 foot table?

Unfortunately it is fairly common to start with the primary form in an orientation that puts the two vp’s inconveniently far apart. In the previous cube construction example, assuming a 10 foot circle of view, the cube is oriented so that the two vp’s would about 11 feet apart — one 3.2 feet to the left of the dv, and the other 7.7 feet to the right. This isn’t very convenient for a drafting table.

If those alternatives don’t appeal to you, then you can rescale the drawing.

How do you define the crucial distance dc (from the direction of view to a vanishing point) in the first place? The easiest method is to use my vanishing point calculator to get the measurements of the vp’s and mp’s, and adjust the viewing distance to the object and your angle of view until you get the proportions that seem desirable.

Or, as described above, you can reduce the circle of view to a workable size, use the method for rotating the vanishing points to determine the locations of vp1 and vp2, measure the distance from these to dv on the diagram, then scale those distances back to life size.

Unfortunately this method, even after you get the hang of it, still forces you into a lot of poking of a pocket calculator, and is hopelessly tedious and prone to error if many lines must be inserted in your drawing. The ultimate solution is to generate a recession grid for the distant vanishing point, and use this grid to determine the perspective reduction for any verticals in the drawing.