Perspective Drawing with Lazy Nezumi Pro
If you want to draw convincing 3d environments, vehicles, and even people, mastering perspective is a must. Traditionally, setting up for a perspective drawing can be tedious and time consuming, with vanishing points going way off the page, and messy construction lines everywhere. Lazy Nezumi Pro's perspective preset will hopefully make this process faster and easier!
This particular preset uses a type of projection called Linear Perspective (Isometric and Fisheye projections are also available as different presets). It generates a set of rulers that connect your current pen position to fixed vanishing points. Your lines then snap to these rulers when you draw, helping you quickly construct perspective-correct objects in your scene.
If you open the Ruler - Perspective preset's Rulers section, you'll see several configurable parameters. This section will explain what these parameters do, and how to choose appropriate values for your perspective drawings.
1.1 Image Zoom
Since Lazy Nezumi Pro does not know the zoom level of your canvas, you must set this parameter to match its value when you zoom in or out, or the perspective lines will no longer align with your scene. It's also recommended to draw a mark under the view center point in a separate layer, so you can realign your image.
While automatic zoom tracking is currently not possible, you can enable the Settings/Spacebar Pan Offsets Ruler Centers menu to keep your center aligned while you pan your canvas (in Photoshop, be sure to uncheck Enable Flick Panning in the general preferences tab).
1.2 View Radius
This is the first parameter you should adjust when setting up for a new perspective scene. It defines the radius (in screen-space pixels) of the circle which is the intersection of the cone of vision with the image plane. You should set this parameter so that the view circle covers most of your canvas at 100% zoom.
The center of this circle is the intersection of the direction of view (or line of sight) with the image plane. It can be moved by dragging the little overlay circle graphic, or by using a keyboard shortcut.
1.3 View Angle
This represents the field of view that is visible within your viewing circle. A small value for this parameter will produce a telescopic view, where the perspective effect is minimized (vanishing lines will seem parallel). A larger value is equivalent to a wide angle camera lense, and will project more of the world to your view circle. Note that objects drawn further out from a 60 degree viewing circle can start to appear unnatural and distorted, but this can be used for artistic effect.
Choosing an appropriate value for this parameter really depends on what kind of scene you are drawing. Typically, you will use a larger value for landscapes, and a smaller value for close-up shots. If you are unsure, try drawing some test scenes at both extremes to get a feel for the difference. With a large field of view, closer objects will appear much larger than they actually are. You may also want to study photographs taken with both wide angle and telephoto lenses. The smaller the focal length of a camera lens, the wider the field of view.
If you want to draw with a 180 degree field of view, be sure to check out the Fisheye Perspective preset!
1.4 View Tilt
This parameter controls the vertical tilt of the line of sight. It corresponds to the angle of rotation around the x axis, and directly controls the orientation of the third (green) ruler.
- When set to 0, the view direction is parallel with the ground, and all the lines going straight up and down in the scene are drawn completely vertical and parallel on the canvas.
- Positive values make the line of sight point towards a point below the horizon. This is sometimes referred as "bird's eye view". In this case, the lines going up and down will not be parallel on the canvas, and will meet at a vanishing point below the horizon line (which will now be above the center of the view).
- Negative values make the line of sight point towards a point above the horizon. This is sometimes referred as "worm's eye view". In this case, the lines going up and down will not be parallel on the canvas, and will meet at a vanishing point above the horizon line (which will now be below the center of the view).
1.5 VP1 and VP2 Angles
These parameters control the angles of the first two perspective rulers. Contrary to the vertical ruler (controlled via View Tilt), these are used for drawing lines that are parallel to the ground. They are defined by their angle with respect to the line of sight.
VP stands for Vanishing Point. In linear perspective, most 3d parallel lines converge to one projected 2d vanishing point. The exception is for 3d parallel lines that are perpendicular to the view direction. These will remain parallel after 2d projection. For example, if you set VP1 Angle to 90 or -90, you will get a perfectly horizontal line that never reaches the horizon. Otherwise, their vanishing point will be somewhere on the horizon line. At 0 degrees, the vanishing point will be at the center of your view.
Controlling the rulers via their angles allows you to place rotated shapes anywhere in your scene, without worrying about where the actual vanishing points should be placed. For example, if you want to draw a square, the only requirement is that the difference between VP1 and VP2 angles is 90. But they can be rotated any way you like: -45/45, -30/60, -10/80, etc.
While the view parameters (radius, angle, and tilt) should not be changed after you've setup your scene view, having some variation in the orientation of your objects by changing VP1 and VP2 angles will go a long way in making it appear more natural. To speed things up, these angles can be rotated together (maintaining their separation angle constant) or separately via keyboard shortcuts, or via their control points while holding the control key.
You can't use VP1 or VP2 for inclined lines that are not parallel to the ground, such as ramps and roofs. Instead, you should construct an axis aligned bounding box using the perspective rulers, and then switch to a different ruler preset such as Parallel Lines, Connected Lines, or Radial Lines, to draw them. Be sure to use separate layers for your internal construction lines, so you can easily hide them at the end.
1.6 Line Snap Mode
The Line Snap Mode parameter determines which ruler is chosen when you draw:
- Off: No snapping. You can draw freely while the rulers are still displayed.
- Auto Detect: The ruler will be chosen automatically based on the direction of the first few samples of your line.
- Manual: You select which ruler to use. You can cycle through the 3 lines by pressing the shift key.
2. Measure Points
The tick markers on the rulers are called Measure Points. These will let you measure and compare relative distances in your 3d scene. In the Overlay Settings, you can set their quantity, size, and unit distance. You can also change the unit distance via keyboard shortcut, which will come in handy later.
You can choose to ignore them or turn them off, but if the relative proportions of objects in your scene are important, then you'll need to understand how to use them.
2.1 Understanding Tick Spacing
Since an infinite number of 3d points can project to the same 2d point, the system can not know the depth of your pen position in the 3d scene based on its 2d screen position. Because of this, the chosen convention is to have the depth be equal to the image plane's depth for all 2d screen positions when you are not drawing. Only once you start drawing can the system know the current depth of your position on the line (relative to its start), and so you will see the ticks get closer together as you near the horizon, or further apart if you draw away from the horizon.
A side effect of this is that the same number of ticks will not necessarily represent the same 3d distance if measured from different 2d screen positions. This would only be true if the 2d positions were at the same depth in the scene, like the two ends of a vertical line (assuming the view has no vertical tilt).
The following image illustrates this. Note how the sides of the cube measure 3 ticks if measured from a front corner, but only 2.5 ticks if measured from a back corner.
2.2 Constructing a Box
Because of this, if you are drawing a 3d object while using measure points to set its dimensions, you will want to count ticks from the same 2d screen position. For example, if you wanted to draw a 3x4x5 box, you would choose a corner, then draw a 3 tick line in one direction, then draw a 4 tick line and a 5 tick line in the other directions, always starting from the same corner. Once your 3 main corner lines are drawn, you can then ignore the measure points when drawing the remaining lines (since you'll be starting from different 2d positions, the tick distances won't match). Instead, you should simply draw until an opposing ruler lines up with the end of an established corner line.
2.3 Extending Sections
If you do want to draw while measuring from a different corner, you'll need to adjust the measure point unit distance. For example, if you wanted to double one of the dimensions of the box, you can place your pen over the desired center corner, and use the shortcut to change the measure point unit distance until a tick marker lines up with with the starting corner. You can then count the number of ticks between these corners, and draw a line on the other side using the same number of ticks.
While it's important to know the previous method, there is another method that is sometimes faster. If you enable Freeze Mode (via keyboard shortcut) while your pen is over a corner of your object, you will get a fixed frame of reference at that position, and a new set of rulers (without measure points) will start following your pen. You can now find the right distances by lining up the rulers with the fixed measure points.
2.4 Subdividing Sections
While in Freeze Mode, you can also quickly divide a section into equal parts. Simply change the measure point unit distance until the section is cut into the desired amount of parts, and line up the new rulers to draw them. This method can be used to quickly find the center of a section, without having to draw diagonals.
2.5 Perspective Symmetry
When working in perspective, foreshortening can make it difficult to estimate the proportions of symmetric objects, especially when they aren't simple boxes. This is another thing Measure Points and Freeze Mode can help you with.
For example, if you want to make sure you are drawing the other side of a symmetric curve correctly, you can use the measure points and the perspective ruler guide lines to project a number of points from the curve to the other side of the symmetry axis.
First, you enable Freeze Mode at a position where one of the axis aligns with a side of your bounding rectangle (in the following example, the red horizontal axis lines up with the bottom), and another axis is at the center of the rectangle (in the example, the blue vertical axis will be the axis of symmetry). You then change the measure distance so that you have a couple tick markers on each side of the symmetry axis (three is usually good, but you may need more if you have a complex curve). At each of these tick markers, you line up the vertical ruler and find the corresponding point on the curve. From that point, you draw a line until the vertical ruler lines up with the corresponding tick marker on the other side. You can then use these projected points as guides when drawing the other half of the curve.
2.6 Perspective Circles
Another thing that can be tricky is drawing circles in perspective. It's important to try to get this right however, or the viewer will immediately know that something is wrong with the drawing.
Viewed in perspective, a circle appears as an ellipse. This is great, as an ellipse is not hard to draw (and you can use Lazy Nezumi Pro's Concentric Ellipse preset), but you still need to figure out how to correctly set the center, degree, and rotation, for it to look right.
As you get more practice at drawing in perspective, you will develop a feel for the correct shape and orientation of the ellipse required. Remember that it doesn't have to be perfect, it just has to look right. Here are some tips that will hopefully help:
- The center of the ellipse will almost never match with the center of the circle, but it's a good starting point.
- Ignore the major axis of the ellipse. It almost never intersects anything useful.
- The minor axis of the ellipse should be loosely aligned with a line coming out of the circle center, which is perpendicular with its plane (like a wheel axle). Note that the further out you are drawing from the view center, the less they will align.
- The ellipse should touch the perspective center point of each side of the circle's bounding square.
- The ellipse should also touch the four corners of a concentric square that is 7/10 the size of the bounding square. You can easily construct this square by changing the measure point unit distance so that you have 10 tick marks on each side of the center, and then count 7 ticks from the center for each side (in the following example, we used a little under 3/4 for clarity). This step gives you four additional points to line up with, and can help fine tune the placement.
3. Further Study
The techniques described in the previous section can be used to build complex objects in perspective. You can either start with a bounding box and cut sections into it (like sculpting), or you can start with XYZ plane views, and project out from them (like building a model skeleton). This is generally called form building.
You can use these techniques as much as needed: sparingly to just make sure you have the correct general proportions, or more like an architect planning exact placement and dimensions of all the elements in a scene (altough at that point, it might make sense to use 3d software).
Also be sure to check out Rene Aigner's excellent video: The Power of Boxes, in which he uses these techniques to draw vehicles:
4. Keyboard Shortcuts
This preset has several useful keyboard shortcuts that can be assigned via the Settings->Edit Shortcuts menu's Constraint Shortcuts tab. Please note that these shortcuts will not override any functions that are already assigned to keys in your art application, so you'll want to use keys that don't already have a function. These will be active as long as the Settings->Constraint Param Shortcuts menu is checked. You don't have to set keys for all of these, but depending on how you work, you might find some of them very useful.
- Move Center: Hold key down while moving your pen to move the center of the current constraint preset (this works with any script that uses a center position).
- Perspective - Rotate VP1: Hold key down while moving your pen from left to right to rotate VP1 continuously.
- Perspective - Rotate VP2: Hold key down while moving your pen from left to right to rotate VP2 continuously.
- Perspective - Rotate VP1 & VP2 (continuous): Hold key down while moving your pen from left to right to rotate VP1 and VP2 together continuously.
- Perspective - Rotate VP1 & VP2 (fixed increment): Two shortcuts to rotate VP1 and VP2 together in fixed increments. You can set the angle of rotation for each direction.
- Perspective - Rotate vertical tilt: Hold key down while moving your pen up and down to rotate the vertical tilt of the view.
- Perspective - viewRadius: Hold key down while moving your pen from left to right to change the view radius.
- Perspective - viewAngle: Hold key down while moving your pen from left to right to change the viewing angle (field of view).
- Perspective - Freeze: Press key to toggle freeze mode, to create a fixed frame of reference at your pen position.
- Measure point unit distance: Hold key down while moving your pen from left to right to change the measure point unit distance.
- Snap Line: When the snapMode param is set to 1 (manual), this key will change the current line your pen will be snapping to when you draw.
If the center of any constraint preset goes off-screen and you can't seem to get it back, you can use the Set/Reset Scripting Center Pos shortcuts to reset it. These can be configured via the Settings->Edit Shortcuts menu's General Shortcuts tab. Please note that these shortcuts however are global, and will override any previously set function.
If you want panning with the spacebar key to offset the center automatically, enable the Spacebar Pan Offsets Ruler Centers setting.
You can also control the ruler angles and the measure point unit distance via overlay control points, while holding the control key. Holding the shift key while rotating and angle will clamp it to 5 degree increments.