Boolean Operations

In 3D and solid modeling, boolean functions refer to operations that are performed on solid objects to create new shapes by combining, subtracting, or intersecting them.

2D Boolean Functions

Ribbon : Modify | 3D Modifications | 3D Boolean

Default Menu : Modify | Modify 3D Objects | 3D Boolean Operations

Palette : 3D Model | Boolean & Facet

Boolean is the name given to the method of combining or separating objects which intersect or are adjacent.

Boolean operations can only take place when working with 2 like objects – for example 2 solids or 2 surfaces.

The first object selected is referred to as the Primary Object ; the second object selected is referred to as the Secondary Object or the Subtracting Unit.

2D Boolean functions perform the same functions on closed 2D sketch profiles as 3D Boolean functions perform on 3D objects. For example, sketch profiles can be added, subtracted or intersected to create new regions.

2D Add

2D closed profiles can be added, subtracted or intersected using 2D boolean functions.

When using 2D boolean functions, both 2D entities should be on the same Workplane.

In the tiles below, the result of the boolean functions can be seen after Add, Subtract and Intersect were performed on the original shape, shown below.

Original Shape

 

Using 2D Add 

 

Using 2D Subtract 

 

Using 2D Intersect 

  

Worked Example

Set the view to World Plan and set the Workplane to Plane by World.

Draw a 2D rectangle which measures 80 x 20, shown below.

Draw a 2D circle using the midpoint of the top edge to define the center and the midpoint of the bottom edge to define a radius of 40, shown below.

Select the 2D Add tool from the Boolean Facet palette and select the sketch profiles in any order. The result is shown below.

2D Subtract

This 2D Boolean function creates a new profile by subtracting the area of one intersecting region from another.

Both profiles must reside on the same Workplane.

Example

A 2D circle to a diameter of 20 is drawn inside the profile shown below.

The 2D Subract boolean function was performed by first selecting the primary region, shown below left, then the subtracting region, below right.

The result is shown below.

Result of new region created by subtracting circle from outer profile

 

2D Intersect

This boolean function creates a region of 2 intersecting closed profiles.

In the example below, the illustration on the right has been produced by performing the 2D Intersect boolean function on the 2 profiles.

Area shown above middle is the common region

3D Add

Ribbon : Modify | 3D Modifications | 3D Boolean | 3D Add

Default Menu : Modify | Modify 3D Objects | 3D Boolean Operations | 3D Add

Palette : 3D Model | Boolean & Facet | 3D Add

This 3D boolean function combines the volume of 2 intersecting or adjoining 3D solids or surfaces.

Example

When two volumes are combined, the properties of the first selected object will take precedence. In the example below, the order of selection is shown below left, with the result shown below right.

Volumes of solids combined using 3D Add

 

Combining Separate Volumes

The volumes of two non-connected or intersected solids can be added, creating a combined volume of both parts. The parts are not physically joined during this process.

In the example below, parts 1 and 2 will be combined to create a single volume of both parts.

By using the 3D Add tool and selecting the units shown above, the volumes will be combined such that the properties of the first selected object take precedence and a sub-unit is created from this union, shown in the Part Tree of the Selection Info palette below.

3D Subtract

Ribbon : Modify | 3D Modifications | 3D Boolean | 3D Subtract

Default Menu : Modify | Modify 3D Objects | 3D Boolean Operations | 3D Subtract

Palette : 3D Model | Boolean & Facet | 3D Subtract

This boolean function subtracts a secondary solid from an intersecting primary solid (subtrahend)

Example

In the example below, box 2 was subtracted from box 1. The order in which the units were selected is shown below.

The result is shown below right.

Unit 2 subtracted from the volume of unit 1

In the example below, the selection order was reversed, producing the result shown below right.

Unit 2 used as the subtracting unit to subtract volume from unit 1

3D Intersect

Ribbon : Modify | 3D Modifications | 3D Boolean | 3D Intersect

Default Menu : Modify | Modify 3D Objects | 3D Boolean Operations | 3D Intersect

Palette : 3D Model | Boolean & Facet | 3D Intersect

This boolean tool creates a new solid from where 2 intersecting 3D objects intersect.

 

Example

In the example below, a Box and Cylinder intersect as shown from World Plan view (below left) and Isometric South West view (below right)

The area shown in green by the arrow is the intersecting region of the 2 solids.

The objects, when selected in any order using the 3D Intersect tool, will create the shape shown below right.

Shape produced from intersecting solids

Updating Boolean Edited Objects using the PART TREE

When 3D objects are combined (3D Add), extracted (3D Subtract) or a new object created using a common region (3D Intersect), their individual shapes are modified according to the task performed.

When Boolean functions are performed on these objects, the Selection Info palette, using the Part Tree History is used to modify the original components which comprise the combined unit.

Example

In the example below, a Sphere is inserted onto the vertex of the Box shown below left. The Sphere is used to extract volume from the Box using the 3D Subtract tool. The result is shown below right.

Sphere used to subtract volume from the Box

The Part Tree of the Selection Info palette is used to modify the original components of the part. For example, the radius of the Sphere is shown in the illustration below.

This component is modified in the Part Tree to increase the volume of the subtraction. In the example below, the radius is changed to 50.

Take Note

The Part Tree history is activated using Options > ACIS > Create Editing History (Part Tree)