BAA013 Constructive Geometry

Credit conditions

To obtain credit:

• Unexcused absenses are not allowed.
• You need to score at least 40% in the sum of points for both tests.
• You need to submit 5 correctly drawn exercises.

Materials for lessons

• Materials for lesson 1:
• Ellipse
• Materials for lesson 2:
• Collineation and Affinity
• Materials for lesson 3:
• Monge projection
• Exercises
• Materials for lesson 6:
• Axonometry-theory
• Axonometry-exercises
• Materials for lessons 7-8:
• Plane sections of solids - theory
• Plane sections of solids - exercises
• The intersection of a line with a solid.
• Materials for lesson 9:
• Perspective projection

Exercises to submit

General information:

• draw exercises with a pencil on office paper, each exercise on a separate sheet
• mark them with your name, surname and date of issue
• submit exercises continuously (the recommended submission date is part of the assignment), you will avoid complications at the end of the semester

The assignment of exercises to submit: soon...

Exercises discussed in lessons

Lesson 1 Ellipse

• Introduction to the conic sections

• Point construction, a tangent, osculating circles here.
• Vertex circle and Directrix circle here.
• Tangent to the ellipse parallel to given direction here.
• Ellipse - Tangent to the ellipse passing through the outer point here.
• Ellipse - Trammel construction here.
• More exercises to practise here.

Tests

The maximum of the first test is 15 points. The maximum of the second test is 20 points. To obtain credit you need to score at least 40% (14 points of 35 points) in the sum of points for both tests. There will be an opportunity to do two make-up tests - in the examination period.

• Test 1 (50 min) - lesson 6
• Tasks that can appear on the first test:
  • Tangents to the ellipse parallel to the given direction, tangents to the ellipse passing through the outer point, construction of the ellipse using focal properties
  • The affine image of a square or a triangle, the affine image of a circle, the image of a square in the collineation
  • Monge projection:
    • Basic tasks concerning a plane (a point and a straight line in a plane, traces)
    • Basic problems
    • Distance of a point from a plane
    • Distance of a point from a line
    • Related views of an object in a plane (a square, a triangle, a circle)
• Sample first test

• Test 2 (50 min) - lesson 11
• Tasks that can appear on the second test:
  • Orthogonal axonometry:
    • Axonometric view of a point.
    • Axonometric view of an object in a first projection plane (a square, a triangle, a circle).
    • Plane section of prism or pyramid with the base in a first projection plane.
    • The intersection of a line with a solid.
  • Perspective projection
    • Construction in the ground plane (lengths, parallels, the angle between intersecting lines...)
    • Perspective projection of a triangle or a square in the ground plane.
    • The tipped ground plan method.
    • Construction - an inaccessible vanishing point, reduced distance.
    • Perspective projection of a solid with the base in the ground plane.
• Sample second test