Today I will show you how to draw Niall Horan from One Direction. Niall is a teen heart throb who has stolen many a girl’s heart with his good looks and amazing singing voice. Find out how to draw Niall with easy steps in the following lesson.

## How to Draw Niall Horan from One Direction with Step by Step Drawing Tutorial

## Step 1

Draw a perfect circle by tracing a lid or using a protractor.

## Step 2

– Draw guidelines half way thru both ways.

## Step 3

– Find half way point again.

## Step 4

## Step 6a

– Draw lines down from the horizontal half way points.

– Then draw circle from the bottom vertical half way point….draw it the width of the 2 red lines.

## Step 6b

Use the above guidelines to help you draw the face in the right proportions.

## Step 7

– Draw leaf-shaped eyes from the 1/4 point (highlighted in red above).

– Draw 3 circles where the nose should be. Notice the blue notches on the vertical line.

## Step 8

– Draw a sideways capital letter ‘A’ shape on the left eye. Draw a letter ‘c’ shape on the right eye.

– Draw the lower (on the right eye) and upper lids.

– Outline the nose around the circle guidelines.

## Step 9

– Draw ovals inside the eyes…draw the lower eyelid of the left eye.

– Draw the center of the mouth.

– Draw the jawline using the guides.

– Draw details of the eye.

– Draw a curved line in the middle of the top lip. Draw letter ‘s’-shaped curves on both sides of the upper lip.

– Draw the lower lip.

## Step 11

– Draw a the hair guidelines around the head.

– Draw lines for the eye brows.

– Draw letter ‘c’ shapes for the ears.

– Draw a sideways letter ‘j’ shape for the left shoulder.

– Draw a line for the right side of the neck.

## Step 12

– Draw letter ‘M’ shapes and letter ‘V’ shapes for the hair.

– Draw letter ‘c’ shapes inside the ears.

– Draw a letter ‘j’ shape on the right side of the neck.

## Step 13

– Draw 2 more lines and then erase the guidelines.

## Finished Line Drawing of Niall Horan from One Direction with Step by Step Drawing Tutorial

– Add some shading. Since I use drawing software without any smudge tool…I can’t really do a good job shading…so that is why this doesn’t look perfect. But since this is only a black and white line drawing, it doesn’t matter.

I hope this drawing lesson helped you draw Niall. Come back soon for more drawing tutorials.

By the end of the section, you will be able to:

- Explain the rules for drawing a free-body diagram
- Construct free-body diagrams for different situations

The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams have been used in examples throughout this chapter. Remember that a free-body diagram must only include the external forces acting on the body of interest. Once we have drawn an accurate free-body diagram, we can apply Newton’s first law if the body is in equilibrium (balanced forces; that is, [latex]

In Forces, we gave a brief problem-solving strategy to help you understand free-body diagrams. Here, we add some details to the strategy that will help you in constructing these diagrams.

#### Problem-Solving Strategy: Constructing Free-Body Diagrams

Observe the following rules when constructing a free-body diagram:

- Draw the object under consideration; it does not have to be artistic. At first, you may want to draw a circle around the object of interest to be sure you focus on labeling the forces acting on the object. If you are treating the object as a particle (no size or shape and no rotation), represent the object as a point. We often place this point at the origin of an
*xy*-coordinate system. - Include all forces that act on the object, representing these forces as vectors. Consider the types of forces described in Common Forces—normal force, friction, tension, and spring force—as well as weight and applied force. Do not include the net force on the object. With the exception of gravity, all of the forces we have discussed require direct contact with the object. However, forces that the object exerts on its environment must not be included. We never include both forces of an action-reaction pair.
- Convert the free-body diagram into a more detailed diagram showing the
*x*– and*y*-components of a given force (this is often helpful when solving a problem using Newton’s first or second law). In this case, place a squiggly line through the original vector to show that it is no longer in play—it has been replaced by its*x*– and*y*-components. - If there are two or more objects, or bodies, in the problem, draw a separate free-body diagram for each object.

*Note:* If there is acceleration, we do not directly include it in the free-body diagram; however, it may help to indicate acceleration outside the free-body diagram. You can label it in a different color to indicate that it is separate from the free-body diagram.

Let’s apply the problem-solving strategy in drawing a free-body diagram for a sled. In (Figure)(a), a sled is pulled by force **P** at an angle of [latex] 30\text <°>[/latex]. In part (b), we show a free-body diagram for this situation, as described by steps 1 and 2 of the problem-solving strategy. In part (c), we show all forces in terms of their *x*– and *y*-components, in keeping with step 3.

**Figure 5.31** (a) A moving sled is shown as (b) a free-body diagram and (c) a free-body diagram with force components.

**Is ideating, tracing, or prototyping on your iPad or iPhone the beginning of your Design workflow?**

Check out Adobe Illustrator Draw – an app for your iPad or iPhone. Draw incorporates your favorite vector drawing tools and features into a streamlined, modern interface. You can draw lines, shapes, and freeform illustrations and with ten drawing layers and a photo layer. And when you’re back at your desk, Creative Cloud connectivity makes it easy to apply finishing touches in Illustrator or Photoshop.

Important Reminder:

Adobe Illustrator Draw will no longer be available for download on the App Store and Google Play Store starting July 19, 2021. If you already have the app installed, you can continue to use it until January 10, 2022. To enjoy an interruption-free experience with similar and enhanced features, try Adobe Fresco for free. Your Draw assets will be automatically migrated when you first sign in to Fresco.

Vector graphics (sometimes called *vector shapes* or *vector objects*) are made up of lines and curves defined by mathematical objects called *vectors*, which describe an image according to its geometric characteristics.

You can freely move or modify vector graphics without losing detail or clarity, because they are resolution-independent—they maintain crisp edges when resized, printed to a PostScript printer, saved in a PDF file, or imported into a vector-based graphics application. As a result, vector graphics are the best choice for artwork, such as logos, that will be used at various sizes and in various output media.

The vector objects you create using the drawing and shape tools in Adobe Creative Cloud are examples of vector graphics. You can use the Copy and Paste commands to duplicate vector graphics between Creative Cloud components.

As you draw, you create a line called a *path*. A path is made up of one or more straight or curved *segments*. The beginning and end of each segment are marked by *anchor points*, which work like pins holding a wire in place. A path can be *closed* (for example, a circle), or *open*, with distinct *endpoints* (for example, a wavy line).

You change the shape of a path by dragging its anchor points, the *direction points* at the end of *direction lines* that appear at anchor points, or the path segment itself.

**A.** Selected (solid) endpoint **B.** Selected anchor point **C.** Unselected anchor point **D.** Curved path segment **E.** Direction line **F.** Direction point

Paths can have two kinds of anchor points: corner points and smooth points. At a *corner point*, a path abruptly changes direction. At a *smooth point*, path segments are connected as a continuous curve. You can draw a path using any combination of corner and smooth points. If you draw the wrong kind of point, you can always change it.

**A.** Four corner points **B.** Four smooth points **C.** Combination of corner and smooth points

A corner point can connect any two straight or curved segments, while a smooth point always connects two curved segments.

Don’t confuse corner and smooth points with straight and curved segments.

A path’s outline is called a *stroke*. A color or gradient applied to an open or closed path’s interior area is called a *fill*. A stroke can have weight (thickness), color, and a dash pattern (Illustrator and InDesign) or a stylized line pattern (InDesign). After you create a path or shape, you can change the characteristics of its stroke and fill.

In InDesign, each path also displays a *center point*, which marks the center of the shape but is not part of the actual path. You can use this point to drag the path, to align the path with other elements, or to select all anchor points on the path. The center point is always visible; it can’t be hidden or deleted.

When you select an anchor point that connects curved segments (or select the segment itself), the anchor points of the connecting segments display *direction handles*, which consist of *direction lines* that end in *direction point*s. The angle and length of the direction lines determine the shape and size of the curved segments. Moving the direction points reshapes the curves. Direction lines don’t appear in the final output.

A smooth point always has two direction lines, which move together as a single, straight unit. When you move a direction line on a smooth point, the curved segments on both sides of the point are adjusted simultaneously, maintaining a continuous curve at that anchor point.

In comparison, a corner point can have two, one, or no direction lines, depending on whether it joins two, one, or no curved segments, respectively. Corner point direction lines maintain the corner by using different angles. When you move a direction line on a corner point, only the curve on the same side of the point as that direction line is adjusted.

A differentiable function–and the solutions to differential equations better be differentiable–has tangent lines at every point. Let’s draw small pieces of some of these tangent lines of the function :

Slope fields (also called vector fields or direction fields ) are a tool to graphically obtain the solutions to a first order differential equation. Consider the following example:

The slope, y ‘( x ), of the solutions y ( x ), is determined once we know the values for x and y , e.g., if x =1 and y =-1, then the slope of the solution y ( x ) passing through the point (1,-1) will be . If we graph y ( x ) in the x – y plane, it will have slope 2, given x =1 and y =-1. We indicate this graphically by inserting a small line segment at the point (1,-1) of slope 2.

Thus, the solution of the differential equation with the initial condition y (1)=-1 will look similar to this line segment as long as we stay close to x =-1.

Of course, doing this at just one point does not give much information about the solutions. We want to do this simultaneously at many points in the x – y plane.

We can get an idea as to the form of the differential equation’s solutions by ” connecting the dots.” So far, we have graphed little pieces of the tangent lines of our solutions. The ” true” solutions should not differ very much from those tangent line pieces!

Let’s consider the following differential equation:

Here, the right-hand side of the differential equation depends only on the dependent variable y , not on the independent variable x . Such a differential equation is called autonomous . Autonomous differential equations are always separable.

Autonomous differential equations have a very special property; their slope fields are horizontal-shift-invariant , i.e. along a horizontal line the slope does not vary.

What is special about the solutions to an autonomous differential equation?

Here is an example of the logistic equation which describes growth with a natural population ceiling:

Note that this equation is also autonomous!

The solutions of this logistic equation have the following form:

As a last example, we consider the non-autonomous differential equation

Now the slope field looks slightly more complicated.

Here is the same slope field again. What is special about the points on the red parabola?

### If you would like more practice, click on Example.

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