3D Drawing. Single Point Perspective with Diminishing Spaces


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1 3D Drawing Single Point Perspective with Diminishing Spaces The following document helps describe the basic process for generating a 3D representation of a simple 2D plan. For this exercise we will be using single point perspective with the VP (Vanishing Point) centred both horizontally and vertically. This will be the eyelevel view point for the drawing. To enable resonably accurate placement of the construction details as well as helping with proportional heights I ve divided the plan into a 1 metre square grid. We ll also use diminished spacing to enable an accurate spacing of the horizontal and vertical lines as they fall away towards the VP. First a few definitons. 2D 2 dimensional geometry. The flat top view of an image. With Garden Design often referred to as the Plan View. 3D  3 dimensional geometry. Drawings with views diplaying life like width, length and height proportions. Vanishing Point  A vanishing point is a point in a perspective drawing to which parallel lines appear to converge. Horizon Line  A horizontal line that divides a scene into top and bottom, earth and sky. Also the line on which one and two point Vanishing Points reside. Perspective Drawing  Views using vanishing points and foreshortening to give a reallife view of a 3D scene on a flat piece of paper. One and Two point perspective retain vertical lines while horizontal lines recede or converge towards the VP (s). Diminishing Spacing  In a perspective drawing, a way to calculate evenly spaced objects as they recede towards the vanishing point To begin, first get your 2D plan. The plan itself does not need specific dimensions as a grid will help place items. For this exercise the boundary is 11 x 13 meters. That s the area from the bottom of the plan to the front of the house.
2 Over this plan draw a grid of equal sized squares. Each square has to represent 1 square meter. This will be used to align our 3D elements on our one point perspective drawing. In the sample above I ve extended the grid with a one meter overlay on the bottom and have extended over to the back of the house as well. This doesn t serve any purpose for this exercise but will in the next. To have your final image nicely centred place your grid evenly
3 over the 2D plan. It s better to have an even overhang on both sides rather that one flush edge and a overhang on the other. If you re doing this by hand drawing, it s easier to do all the first section (up to the point where you start the actual drawing) on normal paper. Once you have the entire grid work done place a piece of tracing paper over the top and fix it down. Then draw the actual 3D view of the garden on this. This way you won t have to erase lots of working lines later. Given we now have a grid we will use a horizontal line marked at 1 meter increments to set our front plane. This should be 11 x 1 meter segments wide (to represent 11 meters). Do the same with a vertical line 3 meters high as in the picture below. It should be 11 segments by 3. The 3 vertical segments will cover the height from the ground to the highest tree in our drawing. This could have been more if the tree heights had been larger. Within this grid draw a horizontal line from left to right through the centre. (Yellow line below) This will be our horizon line. Then a vertical line from top to bottom through the centre: The point where these two lines cross will be our VP (Vanishing point)
4 Next we draw diagonal lines from each intersection point along the bottom of the grid through to the VP in the centre. (Red lines below). Also draw a diagonal line from the top left and the top right to the VP as well. Also draw the top horizontal to complete a frame. So as not to make the following pictures too confusing with colours, I have removed the purple horizontal and vertical lines. It s assumed that you have these drawn at this point. Now we need to create the base horizontal and side lines to gives us the grid going backwards towards the VP. In order to make this drawing accurate we need to ensure these lines diminish at an even rate. Even though we cannot (not here anyway) get an exact measurement for each square by using a measuring tool, we can set a regular diminishing progression between each subsequent vertical and horizontal line as they recede towards the VP. To do this we need to set the first gap. Using this procedure setting the first gap is always a best guess. Draw a vertical line from the first bottom left point to the top of the grid. (Green line)
5 Next draw another vertical line a little way further along the bottom perspective line. If you use a gap just a little shorter than the length of a 1 meter segment across the front this will be closest to get the correct step. Here I have used a little wider gap so I can exaggerate the perspective to make it a little easier to see. It s only this first gap you have to estimate. Now measure the midpoint of the first vertical line and draw a diagonal from this point back to the VP (Vanishing point). In this case the line will be horizontal. (Green horizontal line) Draw a diagonal line (Magenta line) from the top of the first vertical through the point where the second and the horizontal lines cross and down to the bottom. The bottom of this line becomes the point where the next vertical begins. We repeat this process until there are 14 vertical lines.
6 We now have a set of even diminishing verticals. See how they shrink in height and are progressively closer together. Next from the bottom of each vertical we can draw horizontal lines from the left side to the right.
7 We now essentially have a 3D grid to start building our backyard. Before we move on here s just a couple of abstract views of the space we are working in. (This is not part of your drawing) Here s a front grid to represent the front plane. The blocks represent shapes in 3D. See how the faces of these blocks on the front grid are square and how the side plains diminish back towards the VP. Also note that for the shapes below the horizon line you see the tops of the boxes and anything above the horizon you see the bottom. This is the same view without the face grid. The other diagonals are perspective lines that start at the intersection of the grid on the face back to the VP. See how these lines give a sense of how the lines converge no matter where you are in the frame.
8 Even though the diminishing horizontals are not measures as such they are reasonably accurate and we can assume we have a 3D grid of 1 x 1x 1 meter squares. Using your original 2D drawing, place the elements by counting the squares and plotting where to build your drawing. If you have some heights (for the beds etc) you can read them off the side grid. Remember the width and heights on the front horizontal and vertical lines are measurable. For example the front the bed against the side grid is about 600mm and the smaller bed in front is about 100mm high. Knowing this you can draw these heights and then draw diagonal lines back to the VP. Then it s just a matter of estimating were the beds end by measuring the meters (counting the horizontal lines) back from the front. As mentioned earlier it s this point where you place a piece of tracing over the previous grid and do your final drawing on that. You can use a single piece of paper but it does have a lot of confusing working lines. ` `
9 I ve placed the house at the 13 meter mark back and estimated its height as 2 meters to the eves and a further 1.5 for the roof. See how small it is in comparison to the front elements. The construction in front of the door is the water feature. I ve made this a little larger than it would normally be just so you can see the top. Remember that in the original 2D view the feature is a circle. The further you move down from top 2D plan view to the 3D side view that shape becomes and ellipse. Its width stays the same but its depth converges. It s a bit of a guess sometimes when you do this by hand. In the next image I ve put some mass representing trees and shrubs for the left hand side. See how using a perspective line back to the VP helps position and size the foliage. Also see how after doing all your accurate line work the vegetation inevitably hides it. Here s the final picture.
10 Though this drawing was done using GardenCAD there is nothing here that can t be reproduced by using a TSquare, Set Square and a ruler
11 Two Point Perspective with Diminishing Spaces In this section we will reproduce the same plan in two point perspective. Two point perspectives are defined by the use of two VP s along the Horizon line. This gives the image a 3 dimensional view with two planes falling away towards their respective vanishing points. Only the vertical lines remain parallel. Given this process essentially uses the same techniques as with single point it s worth doing the single point perspective section first. First we need to grid our 2 plan just we did with single point. Next draw a horizontal line and a vertical line in the centre of your page. Place two marks (Red squares) equal distances from the centre. For this example I have used the same scale as I did in the previous process. So here they are both 5.5 meters left and right from the centre. Then place two more marks (Green squares) to set our vertical top and bottom. In
12 this example where the VP is in the center of the frame this vertical line is the only line we can measure off the plan. All other lines will diminish away to the VP s. Next it s worth drawing a base boundary and a frame. This helps keep the drawing in a boundary. All you need to do then is join the markers as in the next example. Next we draw the diminishing spaces just as we did in the first example, only here we do it towards both VP s First draw two vertical lines equal distances left and right from the center vertical. The distances here are a best guess but given we know what length we are using for a meter, make the gap a meter or a little less. Then draw a diagonal line (Magenta line) from the top down through the crossover point to the bottom line.
13 Then draw a vertical from the bottom of each diagonal up the top perspective line. Continue this pattern along each side. As with the single point example, these gaps are our 1 meter markers. We need eleven along the right boundary and 19 along the left. This will give us 11 x 19. We need to include some extra length down the left plane as this time as we will now see the side of the house. It s worth drawing two diagonal lines back to the left VP from the centre vertical. (Yellow lines) These will give us a 1 meter height marks. Remember as this center line is the only line we can measure, you can mark the start of each of these points with your ruler. Either that or just divide to line into 3. Now we can draw our base grid by joining all the base points back to the two VP s. All the points at the bottoms of the verticals on the left boundary go back to the right VP and visa versa.
14 As you can see this drawing is very busy and is hard to see where you ll fit your drawing. Remember this is just a grid to help find accurate points for your drawing. If you are doing this exercise in CAD it s easier as you can just turn portions on and off by using layers. With hand drawing it s best to draw this part of the exercise on paper then cover it with tracing paper and draw your actual image on that. You ll also find that on large paper this grid is a little easier to read. You may like to use some different colours to help line points up as well. To start your drawing all you need to do now is use the grid points from your 2D grid and replicate them on the 3D plane here. You can use the centre vertical to help get heights. If you mark 600mm (approx) up the center vertical and draw a diagonal back to one of the VP s, that with give you a 600mm gap between line and the base.
15 This is the drawing without the side grid. Next, draw in some plants using a perspective line to help give them the correct proportions and spacing. This is final 2 point perspective drawing. Notice how the side planes fall away to the Vanishing Points. Also from this angle it s difficult to see the curves of the beds and the water feature at the top near the door. Isometric Drawing
16 Unlike perspective drawing which attempts to give a realistic 3 dimensional view on a flat piece of paper, Isometric views give a 3 dimensional view retaining the shape of each plane. There are no vanishing points or lines of convergence in Isometric drawing. In Isometric drawing all vertical lines are drawn vertically and all horizontal lines are offset by 30 degrees. The advantage of this view is that you can easily use the measurements from your 2D view to produce a 3D image that can show accurate measurements or dimensions on the plan. In this document we shall transform the same base 2D plan and produce an Isometric representation of it. Again I have used GardenCAD to produce these drawings as it is easy to rotate the entire plan 30 degrees and use 90 degree tracking to produce the verticals. If you re doing this by hand I ll make a note on any tips you can follow to replicate this approach. First place your drawing on a horizontal plane of 0 degrees. If you are hand drawing don t fix it to the table yet. Next mark the bottom left corner a draw a line 30 degrees up from the horizontal.
17 If you re hand drawing, don t do this directly on your 2D plan. Do it on a piece of paper underneath. All we are doing here is creating a guide to rotate and lineup our plan. Next using the bottom left corner, rotate your plan to the left and line its base along the 30 degree line. If you are doing this on paper you can also find this by using a protractor or your adjustable square. If you re hand drawing fix your plan down at the point and cover with a piece of tracing paper. Complete the next steps on the tracing paper using the 2Plan underneath as a guide. All you will need is a TSquare and a Triangle to complete. Next lift the elements up by drawing 90 degree vertical lines up from the corners of the plan below. Remember that with isometric drawing you can use the actual height measurements.
18 So if you have a bed 600 mm high then draw it that high. I haven t included all the dimensions here so you can make your own. What I used was: Boundary: 19000x (other lengths you can be guided by the 1 meter x 1 meter in the 2 perspective exercises. Bed height (against boundary): 600mm Bed height (smaller one in front): 100mm Water feature height: 1000mm House (from ground to eves): 2000mm Roof (from eves to top): 1500mm Once you have drawn your 90 degree verticals (Magenta lines) you can join the tops to form the sides. (Yellow line) For hand drawings if you set your square to 30 degrees this makes the diagonal drawing quite quick.
19 Next draw your plants. You can use shapes with specific width and height or representations that have the appropriate proportions for the view. If you are using CAD, trim any parts of the original plan that need cleaning up. If you are hand drawing you should be able to lift the tracing paper away and you should have a final Isometric drawing. If you wish you can include measurements or dimensions.
20 Here s the final image without dimensions.
21
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