For 2D modeling components, or when using work planes in 3D models, you may have noticed a subtle yet significant change in how geometry can be created in the software. Using *Sketch* mode, along with constraints and dimensions, you can draw plane geometry and define relations between the geometric entities that you draw. Rest assured, the 2D geometry drawing functionality you have grown accustomed to is still available, but now there are features that enable efficiency like never before.

### Introducing Sketch Mode

Announced with the release of version 5.5 of the COMSOL Multiphysics® software, *Sketch* mode enables you to interactively draw and edit geometry right within the *Graphics* window. The functionality can be used with planar drawings and is available with the core functionality of the COMSOL® software.

*The* Sketch *tab, available under the* Geometry *or* Work Plane *ribbon tabs for 2D or 3D model components, respectively.*

With *Sketch* mode, you can interactively draw a plethora of different types of shapes. How these shapes are drawn is identical to previous versions of the software, but with enhanced visualization, indicators, and functionality.

#### Interactive Drawing

When drawing geometry in the *Graphics* window using *Sketch* mode, all objects are displayed in wireframe rendering until you are working outside of either *Sketch* mode or the geometry nodes in the model tree. This remains true, regardless of the setting chosen for the object type, such as solid, open curve, or closed curve, enabling you easy access to and viewing of all constituent objects.

*Visualization of a solid object while working in* Sketch *mode (left) versus outside of* Sketch *mode (right).*

After opening the *Sketch* toolbar and selecting the type of shape you want to make in the *Draw* section of the toolbar, you can click and move or drag the mouse in the *Graphics* window to form the shape. Several geometric primitives are available to draw through their own respective buttons, and virtually any geometry can be created through the combination of multiple primitive features.

*A rectangle drawn first using the respective shape’s primitive feature, the* Rectangle *button, and then the* Polygon *button. Using the* Rectangle *button, the object is drawn by left-clicking, dragging the mouse to the desired size, and then left-clicking again to complete the drawing. Using the* Polygon *button, the object is drawn through forming line segments for each edge. Upon finishing drawing the last edge, right-clicking completes the drawing.*

The new *Sketch* mode provides interactive and faster drawing options for shapes available in previous versions of the COMSOL® software, such as:

- Interpolation curves
- Bézier curves
- Rectangles
- Squares
- Circles
- Arcs
- Ellipses

There is also new functionality that provides drawing options for geometric shapes and features that were not available to be drawn previously, like polygons, all of which maximize the efficiency with which you can compose the geometry you need.

Fillets can now be sketched interactively by selecting one or more points and then dragging the mouse to create the rounded corners.

*Demonstration of the* Fillet *operation being used. Vertices at sharp corners are selected and then dragged to form the rounded corners.*

The *Composite Curve* feature enables you to interactively put different types of edges together into a single object while maintaining a connection between all of the constituent edges. This feature is automatically generated and added to your geometry sequence when you draw a sequence of different types of edges. You can also utilize this feature manually by selecting the nodes in your geometry sequence that correspond to the connected edges in your geometry, right-clicking, and then selecting the *Composite Curves* feature. This assembles all of the connected yet standalone curve objects selected in your sequence into a single object.

*A composite curve is shown being drawn, first automatically and then manually. When manually assembling objects into a composite curve, you may need to update the setting for the object type first in order to have the menu option available.*

#### Interactive Editing

When editing any objects in the geometry, apart from changing any values in the *Settings* window for an object, you can now also click and drag the object itself, its edges, or a vertex to resize it or change the position of one or more parts of your geometry. You can also press the *Ctrl* and/or *Shift* keys while dragging the mouse to change how other geometric entities in your design move.

*There are many ways with which you can interactively edit your geometry, as demonstrated in this clip. You can click and drag the center of an object to move it, change the size by dragging an edge, or change the size or configuration by dragging a vertex.*

Additionally, if your sketch contains multiple objects and you are not sure which parts belong to which nodes in your geometry sequence, after selecting the geometric entity in question, you can then double-click it. The respective node that the part of your sketch belongs to will automatically be selected within the Model Builder window.

*As each individual geometric entity is double-clicked while in* Sketch *mode, the node corresponding to that part of the geometry is automatically selected in the Model Builder window.*

This comes in handy when you have complicated or complex designs for the geometry of your simulation. From there, you can make changes to its properties manually in the *Settings* window, or change the object right within the *Graphics* window.

#### Guidelines and Indicators

As you use *Sketch* mode, you will notice that there are many visual indicators that will appear in the *Graphics* window as well as over the respective geometric entities you are interacting with. Upon clicking the *Sketch* button, bold grid lines automatically appear at *x*– and *y*-intercepts, providing quick reference to the origin in the grid.

*The* Graphics *window, displaying bold grid lines at the origin upon enabling* Sketch *mode in the geometry.*

When dragging any vertex in your model geometry, you will notice that green grid lines appear when you have dragged the point to be in alignment with other points in your geometry. You will also notice these same lines appear when sketching any new objects in your geometry. This functionality provides guidance on sketching objects in positions relative to each other.

*Green grid lines display in the* Graphics *window when a vertex is dragged or when a new object is sketched to indicate alignment with other vertices.*

As aforementioned, one of the ways you can edit the objects you have drawn, apart from interactively doing so in the *Graphics* window, is by making changes in the *Settings* window. For some geometric primitive features, such as polygons or interpolation curves, when editing the point coordinates, a red circle identifies the corresponding point in the *Graphics* window that you are currently editing, enabling you to see exactly which point you are moving.

*In the* Settings *window for a polygon, selecting any of the cells in the table will result in the corresponding vertex with those coordinates being highlighted with a red circle.*

### Constraints and Dimensions in the Design Module

Available as part of the *Sketch* ribbon tab, there are tools that enable you to apply constraints and dimensions to planar geometry, which can also be done interactively right within the *Graphics* window. This is useful and especially significant when you are drawing or dealing with complex geometries and use cases, for example, if you wanted to parameterize your geometry and subsequently change the values. Instead of needing to come up with and then manually define expressions for the coordinates and dimensions of primitives, you can specify positions, distances, and angles — making the process a lot faster and easier. Note that this functionality is accessible with the Design Module and is not part of the core functionality of the COMSOL® software.

*The* Constraint *and* Dimension *sections of the* Sketch *tab, available with the Design Module.*

Enabling the use of these tools is done through the *Geometry* node by turning on the respective setting in the *Constraint* and *Dimension* section of the *Settings* window.

*The* Geometry Settings *window, wherein the constraints and dimensions functionality has been enabled by selecting* On *from the respective drop-down menu.*

A *constraint* is a requirement placed on geometric entities that is not associated with a value. Examples of this include requiring that two edges be perpendicular to each other or that a line be tangent to a curve. The software has many predefined constraints available for use, such as:

- Parallel
- Perpendicular
- Tangent
- Coincident
- Concentric
- Equal Distance
- Equal Radius

*A region of a simple geometry showing before (left) and after (right) a* Perpendicular *constraint has been applied between two adjacent edges.*

Conversely, a *dimension* is a requirement placed on geometric entities that is associated with a value. Examples of this include setting the value for the radius of an arc or the distance between two points. Parameters and expressions can also be used to define such values, which is useful when running a parametric sweep or parameter optimization (more on this later). Dimensions that are built into the COMSOL® software include:

- Distance
- x-Distance
- y-Distance
- Total Edge Length
- Angle
- Radius
- Position

*A region of a simple geometry showing before (left) and after (right) a* Distance *dimension has been applied to an edge.*

The *Constraint* and *Dimension* features can be applied a few different ways. They can be added manually by selecting the desired *Constraint* or *Dimension* button in the ribbon and then selecting the appropriate geometric entities in the *Graphics* window to which you want to apply the relation. It can also be done with a more automated approach by enabling the *Smart Constraint* mode or *Smart Dimension* mode. With this approach, you select the *Constraints* button or *Dimensions* button in the *Sketch* toolbar; start selecting geometry; and then, based on the geometric entities you select, the appropriate constraint or dimension appears with its respective icon next to your mouse and is then available for you to apply.

Additionally, constraints can also be added automatically while a sketch is edited interactively if the *Use constraints and dimensions* setting is turned on. For instance, dragging a vertex to coincide with another vertex in your sketch would result in a coincident constraint being automatically generated.

Once your sketch is well defined, the geometry is locked and appears in black as opposed to the gray color it displays when it is unlocked and editable. Additionally, a status message displays in the *Geometry* node’s *Settings* window, stating that the sketch is well defined. Note that applying constraints and dimensions to create a well-defined sketch is completely optional, but is recommended for geometric parameter sweeps and optimization.

*The* Smart Constraint *mode is enabled to apply constraints to this arbitrary geometry. Note the status message for the geometry at the beginning of the video. Following this,* Smart Dimension *mode is enabled to apply dimensions to the geometry. Note the status message for the geometry upon applying all of these constraints and dimensions at the end of the video.*

After applying any constraints or dimensions to a geometry, you can always hover with your mouse over any of the representative icons. This will highlight the geometric entities associated with the constraint or dimension in the *Graphics* window. You can also double-click the icon and the respective node in the geometry sequence will automatically be selected. From there, you can choose to edit any properties of the constraint or dimension in the *Settings* window.

*Upon hovering with the mouse over any constraints and dimensions applied to your geometry, the associated geometric entities are highlighted in the* Graphics *window. You can then double-click any constraint/dimension to open and edit its properties in the* Settings *window.*

### Preparing Your Sketch for a Parametric Sweep

Having discussed this geometry functionality in detail, you may be wondering at what points in your design process to implement the use of such features, particularly if you want to study the influence of geometric parameters using a parametric sweep. For such an application, it is advisable to apply constraints and dimensions to the sketch you have drawn so that it is well defined. Doing so ensures that the geometry you sketch behaves in a predictable way when the dimensions are changed. As dimensions and coordinates update according to the values you specify in the sweep, the shape and the relation of geometric entities to each other is maintained.

There is no specific procedure that needs to be employed to bring a sketch not sufficiently constrained and defined to one that is. However, we have found the following order of steps to be useful when drawing and uniquely defining a sketch to be used in a parametric study through the use of the *Sketch* toolbar:

- Sketch the geometry
- Apply constraints
- Apply dimensions
- Apply constraints and dimensions to lock the rigid body degrees of freedom

In the steps outlined above, you can see that applying constraints and dimensions is actually split into two parts: one in which you define and constrain the geometric entities within your sketch, and another in which you define and constrain the geometry specifically with respect to avoiding rigid body translation and rotation. Following this order is generally efficient in obtaining a well-defined sketch. In this way, the geometry itself is constrained first. Then, the last constraints and dimensions needed to result in a well-defined geometry are those that eliminate the sketch from being able to be moved freely as a rigid body. Dimensions such as *Position*, *x-Distance*, or *y-Distance* can be used to constrain rigid body degrees of freedom.

### Next Steps and Further Learning

After learning about this geometry functionality in the software, we encourage you to try it out! Experiment with combining different shapes and employing the recommended sketching workflow mentioned above to become familiar with these invaluable tools.

To learn more about the *Sketch* toolbar as well as the *Constraint* and *Dimension* features, you can refer to the COMSOL Multiphysics version 5.5 Release Highlight pages for Geometry and the Design Module, respectively. In addition, for those users with licensing for the Design Module, there is a tutorial on using the *Sketch* tool along with constraints and dimensions in the *Introduction to the Design Module* documentation.

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