Activity 2.2: Changes of Plane - Perceiving Depth in 2 Dimensions

Activity Description

Students learn how to reveal objects that are behind others in a 3-View drawing when the objects are stacked or layered. They are introduced to the use of shading and Engineering Notation conventions for showing coplanar and non-coplanar surfaces in a 3-view drawings.

Getting Started

Introduction:

E.Q.: How can we represent 3D objects in 2D?

Preparation Needed for the Activity:

Three 1” wooden cubes per student
Small metal ruler
Graph paper
Pencils

Part 1 - Review: 5-10 min

Review: Face, Edge, Vertex
Review: Perspective, Isometric, Vanishing Point
Review: Basic 3-View Drawing

Three-dimensional perspective of three connected cubes. The first cube is labeled front on the front side and right on the right side.The second cube is connected to the left side of the first cube. The last cube is on top of the first cube. The top of the last cube is labeled top.

Figure 1

Part 2 - 3-Cube Challenge - Shading: 15-20 min

Set up 3 large cubes at the front of the room, and have the students set up their own 1” cubes in the same way

(Figure 1)

The students will have trouble with the top view because the two top faces are on different planes; that is, they are not coplanar. This means that the vertices are not all on the same plane (Recall, a plane is a flat surface that extends to infinity). This can be illustrated using a sheet of paper or another flat object such as a pencil. You can balance separate sheets of paper on each top surface, but you can’t balance a single sheet across both top surfaces while keeping contact with all of the vertices.
Introduce shading to help communicate this change of plane/ depth. In this example, the plane that is closest to the person is shaded. Other conventions are okay, but you probably want to be consistent across your classes.

Two-dimensional perspective of three connected cubes. From the top perspective, there's two squares side by side. The right square is shaded. From the front perspective, there's three connected squares forming a backwards L. From the right perspective, one square is stacked on top of the other.

Figure 2

Figure 2: 3-View Solution

Note that the taller cube on the top face is shaded, indicating a change of plane.
Students should shade their drawings.

Part 3 - 3-Cube Challenge - Engineering Notation: 15-20 min

Instruct the students to pretend that the cube structure is a solid object (ie not made of 3 separate cubes). Discuss how they would draw the structure. Specifically, discuss the option of just drawing the faces of the overall cube structure. That is, if a set of cube faces is coplanar, simply draw the outline of the composite shape rather than drawing each individual cube. This is the commonly accepted engineering notation—present on board.
Introduce concept of a "hidden line" (Figure 3)

Two-dimensional perspective of three connected cubes. Solid line represents a visual change of plane. A dashed line is called a hidden line. It indicates a change of plane that is not visible.

Figure 3

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