FREE Lesson 3 - Simple Volumes Projection, Axonometrics And Sketches
Introduction
Simple volumes will help you visually break down and understand buildings, objects, what you see around you and any architecture you might come across. Other than that they offer interesting practice for shading cast and volume shadows - after we understand the logic of how light falls on each of these volumes you will be able to use them to create an abstract architecture composition. We will be going through each of the simple volumes in detail, so you can learn how to draw them in perspective with shading and cast shadows, after that we will draw them in technical drawing (triple projection and axonometric) with shadows. As always, when sketching use the four-step formula: construction lines, contour lines, hatching and re-thickening the line drawing... Because all your drawings begin as freehand sketches, you will improve the quality of your line drawing immensely.1.) Cube
A cube isaprism with length, height and width equal... so it can be created as a prism with only one edge as a variable, so it has six faces which are all squares. The cube will be thesubject of many, many descriptive geometry exercises as it has many interesting geometrical properties: three different positions in triple projection, several sections which represent perfect triangles and hexagons.2.)Prism
A rectangular prism is a volume with six faced and all six faces perpendicular to each other. It can also be created by extruding a rectangle around an extrusion axis; ideally, the extrusion axis being perpendicular on the rectangle. The rectangle can be a polygon with multiple edges, so our prism ends up having a triangle, rectangle or even hexagon for a base. A rectangular prism si defined height, width and length.3.)Triangular Prism
You get a triangular prism by extruding a triangle around a vertical axis. This volume is not very common in descriptive geometry and does not have any particular geometric properties. It could be used for volume intersections: imagine intersecting a triangular prism with a cone, pyramid, cylinder. Another type of descriptive geometry exercise that involves prisms could be around drawing two tangent spheres tangent on the ground and on the triangular prism.4.) Pyramid
A pyramid is determined by its base (which can be any polygon out there) and height (which again can be perpendicular on its base or not). Some of the most common bases for pyramids you will find in descriptive geometry are square, pentagon and hexagon. The most interesting pyramid is the tetrahedron - this is a pyramid with four faces, all of which are even triangles. We will use tetrahedrons for many descriptive geometry exercises as they have particular properties to them as fitting perfectly into spheres or two different specific positions etc.5.)Sphere
You can create a sphere by rotating a circle 360 degrees using one of its diameters as a rotation axis. Spheres will also be the subject of many descriptive geometry exercises. The main issue with spheres is the tangency and equilibrium dilemma - for a sphere to be tangent to a surface or other volume it needs to touch the specific volume at one point. To get equilibrium, you need to have at least three tangency points - one point or two points would be not enough to get full equilibrium. Going back, tangency between two volumes implies the two having an exact point where they touch. This can easily evolve into ‘how can we put a sphere in perfect balance on three cones’, or ‘how can we put a cube in perfect balance on three spheres’ type of problems. These are particularly interesting and will challenge your way of seeing architecture and your problem-solving capabilities.6.) Cylinder
A cylinder is created by rotating a vertical line around a vertical axis for 360 degrees or by extruding a circle around an axis. The defining elements of a cylinder are the base, height, and the fact that the axis is perpendicular to the base or not. Most cylinders we will be drawing have a vertical axis perpendicular on the base, so you need to only worry about the radius of the base and cylinder’s height.7.)Cone
A cone can be created by rotating a random line 360 degrees around a vertical axis; thus it represents a rotation volume. Also, a cone is defined by a circular base and height. The height can be a line in a random position, or it can be perpendicular to the base... In 99% percent of cases, our cones will have the height perpendicular on the base, especially in descriptive geometry.FREEHAND DRAWING
RECTANGULAR PRIMITIVES
1.)Cube
A cube is a box that has all six faces equal squares. Another definition of a cube is that it is a box with the length equal to the width and height. Obviously, all of our drawings are in perspective, so you need to guesstimate these different dimensions as you sketch them.
How To Draw A Cube:
Draw the horizon line, then the two perspective points so we can start constructing all the edges by connecting lines to the perspective points just like in all perspectives we always did until now. For this drawing, you can just use A4 sheets with one sketch/sheet - this way you get a successful drawing. The trick here is getting the proportion just right, that is what will make this box perspective look like a cube. Obviously, you need a bit of practice drawing simple box perspectives and cubes, so you get the proportions right from the first try. What if you could draw 4-5 of these cube perspectives on an A4 sheet each, with their cast shadow and shadowed faces, in all three perspective types: top-down, bottom-up, building view.
2.)Prism
A prism is basically a box in perspective - it will have two vanishing points, and you will see the shadowed face more than the face that is directly hit by light. Also, make it a point of drawing one perspective point on the page and the other off the page - to keep the proportions right for each drawing. In this examples we will draw a triangular perspective, so that will have both the top and bottom pieces triangles.
3.)Pyramid
A pyramid is a simple volume with a rectangular base, height and side faces. Its base can be any sort of rectangular shape - triangle, square, simple rectangle, pentagon, hexagon, octagon, do-decagon, etc. The pyramid’s height can be perpendicular on the base, or it can be at an angle... the most common is the perpendicular height. If it has a circular base technically becomes a cone... so that means in perspective you draw an ellipse and connect it to the height. Constructed shadows are again 60 degrees and a horizontal, the tip of the pyramid casts a shadow on the ground. Hatching-wise we will always go for the same type of cross hathing approach, with the focus on hatching the inclined faces.
How To Draw A Pyramid:
Draw the base in perspective - whatever it is: square, rectangle, triangle, etc. Unite two diagonals for the base, so you get the middle of this shape (the ideal starting point for the height) Construct the height perpendicular on the base (perpendicular to the horizon line, as a reference). Start the drawing from the base up, you can experiment with a pyramid having the base in different vertical planes (the height will now go in perspective) Obviously, another variant is having the height of each pyramid not be perpendicular to the base - this would make an interesting study as well. Also, another variant is drawing each pyramid in a different position in relation to the horizon line... so again top-down, bottom-up, building view perspectives...
CURVILINEAR PRIMITIVES
4.) Sphere
A sphere is what happens if you rotate a circle 360 degrees and around an axis. The sphere, alongside the cube and friends, will be thesubject of many many descriptive geometry exercises. Spheres do not sit in natural equilibrium when not on a horizontal surface... so they require three tangent points for that. This will be the subjects of many descriptive geometry exercises in the future.
5.)Cylinder
A cylinder is what happens if you rotate a vertical line 360 degrees around a vertical axis. The height of a cylinder can be perpendicular on the base, or it can be leaning at an angle.
How To Draw A Cylinder:
Draw the bottom ellipse which is the base of our cylinder. This is done as all horizontal ellipses are, by fitting the ellipse into arectangle which gets flatter as it moves closer to the horizon line. The height of a cylinder usually is perpendicular to the horizon line and then the top ellipse is drawn again as a horizontal ellipse fitting into a rectangle. The other way of drawing a cylinder is by drawing the rectangle which fits its outline, then adding the top and bottom ellipses that add volumetric depth to it. Test out drawing a cylinder which is not sitting upright, but rolling on one side. This means the ellipses are not horizontal ellipses but vertical ones.
7.)Cone
A cone is the equivalent of a pyramid as a curvilinear volume. Cylinders, cones and spheres are curvy volumes so make for excellent tangent descriptive geometry exercises ( this will be a future assignment in drawing and design). Careful when drawing the ellipse that forms the base of our volume - if the base is horizontal then you need to apply the rectangle approach to getting a good ellipse. For a vertical ellipse, you need to fit the ellipse into a rectangle and then use the diagonals and vanishing points to fit the ellipse in seamlessly.
