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 1 drawing.
- You need to submit 10 correctly drawn exercises.
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.
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Test 1 (50 min)
- 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
Make-up test
Content of the make-up test will be the same as in the previous two tests. To obtain credit you need to score at least 40% (14 points of 35 points).
You have two attempts to pass the make-up test. You should see dates of tests in electronic index, please register there.
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:
Drawings
General information:
- Read the assignment carefully!
- Follow the prescribed appearance and format (A4: 210 × 297, A3: 297 × 420, A2: 420 × 594).
- Draw the folded and rotated shapes with dashed and dotted lines.
- Draw the auxiliary structures with dashed lines (it may not be described, but it must not be missing).
- Draw ellipses using osculating circles and a trammel.
- Write all labels (including headings etc.) except indexes ideally using a template.
- Layout of drawings.
Assignment of drawing:
Drawing:
- Write the heading RIGHT CIRCULAR CONE. Do not describe the assignment.
Exercises to practice
- These exercises do not need to be submitted, they serve as preparation fot the tests. They are intended for practicing.
Exercises discussed in lessons
Lesson 1 (Ellipse)
- Point construction, a tangent, osculating circles here.
- Vertex circle and Directrix circle here.
- Tangent to the ellipse parallel to given direction here.
- Tangent to the ellipse passing through the outer point here.
- Trammel construction here.
- More exercises to practise here.
Lesson 2 (Central collineation, affinity)
Lesson 3 Monge projection
- Trace points of a line, the true length of the line segment exercise 1
- Traces of the plane exercise 2
- Basic problem IIb: a point of intersection of a straight line with a plane here
- Basic problem IIIa: a line perpendicular to a plane here
- Distance of a point from a plane exercise 3.
- Horizontal and vertical (frontal) lines, lines of steepest slope here
- Basic problem IIIb: a plane perpendicular to a line here
- Distance of a point from a line exercise 4.
- More exercises to practise here.
Lesson 4 Monge projection
- Rotation of the point lying in the plane here
- Equilateral triangle here.
- Exercises - construction of solids in MP.
- Projection of prism.
Lesson 5 Monge projection - construction and plane sections of solids
- Related views of a circle given by its center and its one point here
- Projection of the cylinder in MP.
- Plane sections of solids - theory and exercises for lesson here
Lesson 6
-
Monge projection - plane sections of solids
- Plane sections of solids - plane section of a pyramid
Axonometry
Lesson 7
-
Test 1 (50 min)
- 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
-
Axonometry
- Regular pyramid with the base in the horizontal projection plane.
- The circle lying in the horizontal projection plane given by the center and one point.
Lesson 8 Axonometry
Lesson 9
- Perspective projection
- Basic facts.
- Perspective projections of straight lines.
- The angle of intersecting lines.
- Reminder of basic constructions known from the lecture:
- Perspective projection of a rectangle in the ground plane.
Lesson 10 Perspective projection
Lesson 11
-
Test 2 (50 min)
- 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
-
Perspective projection
- Perspective projection of stairs
- Similar example.
- The exercise recommended for practicing the tipped ground plan method: the object given by its tipped ground plan.
Lesson 12
Perspective projection
- Perspective projection of crossroad
- Recommended exercise:
Materials for lessons
- Materials for lesson 1:
- Materials for lesson 2:
- Materials for lesson 3:
- Materials for lesson 5:
- Materials for lesson 6:
- Materials for lessons 7-8:
- Materials for lesson 9:
Recommended literature for studying:
• Descriptive geometry - in english (Monge projection and perspective projection)
• CD Deskriptivní geometrie
• A collection of solved exercises from constructive geometry (in Czech).
Here you can find more information and materials to descriptive geometry at FAST VUT
