Modeling with Signed Distance Fields

At the beginning of this learning pathway, you learned why nTop represents geometry as a signed distance field rather than as a set of faces and edges. This lesson looks at what that field actually is, how you look at it, and what you do with it. After completing this lesson, you will be able to:

• Explain how a field contains more information than whether a point is inside or outside a body.
• Describe how a field extends infinitely through space, beyond the implicit body it represents.
• Distinguish between the field itself and its on-screen visualization.
• Explain how union, subtract, and intersect combine multiple fields through arithmetic Boolean operations—and why they behave differently in nTop than in traditional CAD.

​

Signed Distance Fields

A signed distance field (SDF) is a function (i.e. f(x,y,z)) that assigns a value to every point in 3D space based on its distance from the nearest surface of a body and whether the point lies inside or outside that body. As introduced in Lesson 1, the sign indicates the point’s position relative to the surface:

• Negative — the point is inside the body
• Positive — the point is outside the body
• Zero — the point lies exactly on the surface

The magnitude represents the distance to the nearest surface. For example, a point 4 mm outside the body has a value of 4 mm, while a point 4 mm inside the body has a value of −4 mm. Together, the sign and magnitude describe the relationship of every point in space to the body’s surface. Importantly, the signed distance field exists throughout the surrounding 3D space—not only where the body itself exists. Field of a primitive sphere — Positive values outside the sphere, zero at the surface, and negative values inside the sphere. Using the sphere from Lesson 1 as an example — radius 3, centered at the origin: F(x, y, z) = √(x² + y² + z²) − 3 Evaluate it at the origin, and you get −3 mm. That is not an arbitrary number: it is the distance from the center of the sphere to its surface, negative because the origin is inside. Evaluate it 10 mm out along the x-axis, and you get 7 mm. The function returns a real, physical distance everywhere.

​

Isosurfaces

If the body’s surface is defined by the points where the field value equals zero, then any other constant field value also defines a surface. For example, all points where the field equals −1 mm form one surface, while all points where it equals 2 mm form another. These constant-value surfaces are called isosurfaces. Together, they form nested surfaces inside and outside the body, like the layers of an onion. The lines shown in the GIF above represent these isosurfaces for the Field of a Primitive Sphere, with each line corresponding to a constant field value. This concept underpins many implicit modeling operations you will encounter later. Offsetting a body does not require constructing a new surface; instead, the operation shifts which field value defines the body’s boundary. Shelling uses the region between two isosurfaces to define the shell. Similarly, applying a blend radius to a Boolean operation modifies how the underlying fields combine near the resulting surface.

​

Why Distance Matters, Not Just Sign

Any function that is negative inside a shape and positive outside will describe that shape correctly. It will not necessarily be a signed distance field. The distinction matters because the operations above depend on the magnitude being a true distance. If the field says −1 at a point that is actually 4 mm inside the body, an offset driven by that field will land in the wrong place. A well-behaved SDF has a recognizable signature in the Field Viewer: its isolines run parallel to the surface and are evenly spaced, because moving 1 mm through space changes the field value by 1 mm. Crowded or uneven isolines indicate the field has been distorted and no longer measures true distance. You will use this signature as a diagnostic long before you need the underlying math. Course 2 covers what causes a field to stop being a true SDF, and what to do about it.

​

Fields Extend Beyond Solid Bodies

Fields are not exclusive to closed bodies. Simple geometry carries simple fields: Three examples of simple geometries fields: Point field (left), Curve field (center), and a Profile field (right) The plane is the key example to remember. Its field is equivalent to the scalar field z, dividing space into positive and negative half-spaces. This makes it a standard tool for cutting a body in two. An example of a Plane’s field. The normal direction of the plane determines the positive value side of the field

​

Fields are unbounded

Consider the plane in the table again. Where does its field end? It does not. A plane’s field is defined throughout all of space. Even a point one kilometer away still returns a value representing the signed distance to the plane. The same principle applies to the field of a point, a curve, or a sphere. Fields extend infinitely through space . The geometry itself may occupy a finite region, but the field that describes it does not. This behavior often goes unnoticed because many fields you encounter first contain an enclosed negative region. For a closed body such as a sphere, negative field values define a finite volume that nTop can render as solid geometry. The field continues infinitely beyond the body, but it does not display the positive region as material. Not all fields, however, contain an enclosed negative region:

• Plane: Divides space into two infinite half-spaces; neither side is enclosed.
• Triply Periodic Minimal Surface (TPMS) fields: Fields such as gyroid, Schwarz, and diamond repeat indefinitely in all three spatial directions.
• Point and curve distance fields: Remain positive everywhere because a point or curve does not enclose a volume.

The key distinction is that a field can be infinite even when the geometry it represents is finite, or when it does not define a finite solid at all. The field of a Sphere with a radius of 5 An infinite Gyroid Field

​

Giving an Unbounded Field an Extent

When you need to visualize or use an unbounded field as geometry, the Set Bounding Box block assigns it a finite region of interest. The underlying field does not change; the bounding box simply defines the portion of the field that nTop evaluates as a body. For example, applying a bounding box to an infinite gyroid field produces a finite gyroid body that you can visualize and use in downstream operations such as Booleans. Using the Set Bounding Box block to visualize a portion of the Gyroid Field

​

Bounding Boxes Are Estimates

Every implicit body has a Bounding Box property that defines the region containing the body. This box may extend slightly beyond the body’s actual boundaries, which is expected. Because an implicit surface is defined by a field rather than stored explicitly, nTop must determine its extent by searching the field. Computing a perfectly tight bounding box for an arbitrary field can be computationally expensive, so nTop uses a conservative estimate that safely contains the entire body. For a tighter bounding box, use Refine Bounding Box under Utilities in the Modeling tab, or manually use Set Bounding Box with the parameters that control your implicit body. Refine Bounding Box block recomputes the bounding box of an implicit body to a specified tolerance, producing a closer fit around the body’s actual extent. It is particularly useful after operations such as Booleans, where the resulting body’s bounding box may remain larger than the geometry itself. The pink outline shows the original bounding box, while the green outline shows the tighter bounding box produced by Refine Bounding Box

​

How Fields Generate Geometry

Earlier in this learning path, we introduced a fundamental distinction: CAD stores geometry as faces, edges, and vertices, while nTop stores the function that defines the geometry. The surface is generated where that function equals zero. This distinction has several important implications:

• No faces are stored to select or reference, avoiding failures when topology changes or disappears.
• Bodies are watertight by construction because the field continuously defines what is inside and outside.
• Geometric complexity is inexpensive. Adding detail increases mathematical computation, which nTop’s parallel architecture handles efficiently, without introducing the topology or file-size burden associated with the faces and edges of traditional CAD.

​

The Field and Its Visualization Are Not the Same

The SDF defines the geometry; the Viewport visualizes it. The field is a continuous function that returns a value at every point in space. The Viewport samples that function and renders the zero surface according to the selected display resolution. Increasing the resolution from Low to Highest improves the visualization, but it does not change the underlying geometry. This distinction has several important implications:

1. Viewport resolution affects visualization, not geometry. Increasing resolution improves visual fidelity at the cost of render time, but it does not change the underlying implicit body or the quality of geometry exported from it. Use Low or Medium resolution while working and increase it when a closer visual inspection is necessary.
2. Visual artifacts do not necessarily indicate incorrect geometry. Thin walls may appear to have holes, lattice beams may look disconnected, and fine repeating features may display artifacts when the Viewport cannot fully resolve their detail. Use Precise Render (Ctrl + H), increase the Viewport resolution, or enable Adaptive Resolution—introduced in the previous lesson—when you need a more accurate visualization.

A turbine blade visualized using Low Resolution (left) and Highest Resolution (right)

3. When in doubt, probe the field. If the visualization still appears incorrect, use the Field Viewer to inspect the underlying field directly. For example, if a wall appears missing, a negative field value where material is expected confirms the geometry exists—the Viewport is simply not resolving it clearly.

The pattern is consistent: Viewport rendering, Precise Render, meshes, and slice data are all representations generated from the underlying field at a specified level of fidelity or tolerance. The field itself remains exact, and the Field Viewer lets you inspect its values directly. Fields can also do more than define geometry. They can drive parameters such as thickness, radius, and density, allowing these values to vary continuously through space. Course 2 introduces this concept, known as field-driven design.

​

The Field Viewer: Looking at an SDF

The field extends continuously throughout three-dimensional space, so you can’t visualize it all at once. The Field Viewer addresses this by displaying a two-dimensional slice through the field—a window that can be positioned wherever you want to inspect its values. The previous lesson introduced how to access and use the Field Viewer. This section builds on that foundation by exploring its functionality in greater detail.

​

Opening the Field Viewer

With a block selected, press the shortcut key “F”. You can also right-click an object in the Viewport and choose Field Viewer, or open it from the Field Viewer button in the view toolbar. When you open it from a selected block, the Object input is filled in for you. If you open it with nothing selected, the input is empty — type the name of the block whose field you want to inspect.

​

Positioning the window

• Size — how large the plane is. Use the reset button beside the input to fit it to the current view.
• Center and Normal — type values directly, or drag the gimbal in the 3D scene.
• Orientation buttons — the YZ, XZ, and XY buttons snap the normal to a global axis. This is the fastest way to compare the same field from three directions.

The Field Viewer configuration options displayed under the Tools tab of the Right Panel If the plane appears to have disappeared, check its normal direction. A plane viewed edge-on is not visible—for example, looking along the z-axis at a plane with a normal of [1, 0, 0].

​

Reading what you see

• Opacity — Controls the field’s opacity. Drag the slider to adjust its transparency.
• Isolines — white lines connecting points of equal field value, on by default. Leave Interval at 0 for adaptive spacing, or enter a value to fix it. Evenly spaced, surface-parallel isolines are the signature of a healthy SDF. You can toggle this functionality on or off.
• Custom range — clamps the display to a minimum and maximum you choose, giving you fine color resolution in a narrow value band.
• Colormap — Implicit is applied automatically to implicit bodies and is tuned to make the inside/outside boundary legible. Scalar fields default to Turbo; Distance Field is also available.
• Probe Values — Hover anywhere on the plane to view the field value at that point. The corresponding isoline highlights, showing all other points in the slice with the same field value. You can toggle this functionality on or off.
• Show Defects – Highlights field discontinuities as red regions—areas where the field value changes abruptly and may produce artifacts, such as unexpected walls or holes in toolpaths during slicing. You can toggle this functionality on or off.
• Highlight Zero shows a yellow contour where field values equal zero. You can toggle this functionality on or off.

To see the negative region of an implicit body’s field, turn the body’s visibility off with the shortcut key “V”. Otherwise, the solid sits in front of the part of the field you are trying to read.

​

Boolean Operations as a Core Capability

In a B-rep system, Boolean operations are computationally intensive. The software must determine where two surfaces intersect, trim the intersecting surfaces, stitch the remaining regions into a new watertight boundary, and reconstruct the resulting topology. When surfaces are tangent, nearly coincident, or affected by numerical precision issues, this process can become unstable or fail—one reason Boolean operations often cause robustness challenges in traditional CAD workflows. On fields, Boolean operations are arithmetic. Boolean operations are fundamental tools in implicit modeling that allow you to create complex geometry by combining, subtracting, or intersecting implicit bodies. Boolean blocks are located in the Modeling tab of the nTop Ribbon. The Booleans section of the Modeling tab in the Ribbon

​

Boolean Blocks

Boolean Union — Combines multiple Implicit Bodies into a single body, with an optional blend feature between the joining bodies. An example of using Boolean Union to combine two spheres into a single body It natively has an empty Implicit Body List block in its Bodies input. You can either remove it and insert your own list or populate the empty list with your bodies. If you need to combine more than two bodies, you can use the plus sign to add more list items. If you add too many list body inputs, you can remove them using the minus sign next to the list item. Adding a Blend Radius to a Boolean Union smooths the transition between the merged bodies Boolean Subtract — Removes the volume of one or more Implicit Bodies from a primary body. You can apply an optional blend to the resulting edge. An example of using Boolean Subtract to subtract one sphere from another Similar to the Boolean Union block, if you need to subtract more than one body, you can use the plus sign to add more list items. You can apply a Blend Radius to smoothen the edges where the subtraction occurred Boolean Intersect — Creates a new body from the shared, overlapping volume of two or more Implicit Bodies. An example of using Boolean Intersect to create a new body where the sphere’s intersect If you need to intersect more than one body, you can use the plus sign to add more list items. You can apply a Blend Radius to smoothen the edges of the resulting intersection body Clearance — Subtracts one implicit body from another with an added offset distance. An example of using the Clearance block to subtract a cylinder from a box with an added Clearance Distance Pipe Intersection — Creates a blend body at the intersection of two implicit bodies. The radius input controls the size of the blend between the two bodies. An example of using the Pipe Intersection block to create a blend body where the two cylinders meet

​

Blend Type

A blend can be applied where the input bodies intersect to control the transition between their volumes. The available Blend Types are:

• Sharp preserves the original intersection without smoothing.
• Rounded creates a filleted transition.
• Continuous creates a smooth, curvature-continuous transition.
• Chamfered creates a beveled transition.

You cannot adjust the transition angle for the Rounded or Chamfered blend types. For additional information and examples of the blend types available for each Boolean block, see nTop Documentation > Booleans. A visual comparison of the different blend types when using the Boolean Union block The Blend radius input accepts a Scalar Field, not only a number. That means the fillet can be large in one region of the part and small in another. Course 2 covers driving parameters this way.

​

Cutting with a Plane

Splitting, cutting, and trimming are all accomplished the same way in nTop: by performing a Boolean Subtract or Boolean Intersect with a plane. This works because a plane defines more than a flat surface—it divides all of space into two infinite half-spaces. As established earlier in this lesson, the plane’s field is:

• Zero on the plane itself
• Positive on the side toward which the normal points
• Negative on the opposite side

nTop treats the negative half-space as solid material. Therefore, when you subtract a plane from a body, the negative half-space is removed and the portion of the body on the positive side of the plane—the side toward which the normal points—remains. Procedure:

1. Add a Plane or Plane from Normal block, both located in the Create tab under Vectors. A Plane is defined by an origin point and two in-plane axis directions; a Plane from Normal is defined by an origin point and a normal vector.
2. Add a Boolean Subtract block from the Modeling tab.
3. Assign the body to be cut to the Primary Body input.
4. Assign the plane to input “0” of the Implicit Body List. You can use the plane directly here because the Plane type exposes a Body property that nTop reads as an implicit body.

Using Boolean Subtract to cut a Cone in half using a Plane from Normal. The Plane’s field is visualized to show how the negative side is subtracting Because the normal determines which side remains, reversing the normal reverses the result. You can control this in several ways:

• Reverse the normal vector. In the Plane from Normal block, negate the normal—for example, change [0, 0, 1] to [0, 0, −1].
• Use the plane’s Inverted property within the Block Properties. This returns the same plane with its normal reversed.

Using the Plane from Normal’s inverted property chip to subtract the other side of the cone from the previous example

​

What to Take Away

• A signed distance field assigns every point in space a value whose sign indicates whether the point is inside or outside a body and whose magnitude represents the distance to its surface.
• Fields extend infinitely through space. A bounding box defines the region that nTop evaluates and displays without changing the underlying field.
• The Viewport displays a sampled visualization of the field’s zero isosurface. Display resolution affects visual fidelity, not the underlying geometry.
• The Field Viewer allows you to inspect field values, isosurfaces, and potential defects. Evenly spaced, surface-parallel isolines indicate a healthy signed distance field.
• Boolean operations combine fields arithmetically, making unions, intersections, subtractions, and blends more robust than topology-based operations in traditional CAD.
• A plane’s field divides space into positive and negative half-spaces, allowing it to cut an implicit body through a Boolean Subtract or Intersect operation.

​

What’s Next

You have now learned what a signed distance field is, how to visualize and interpret it, and how to perform Boolean operations. Next, you will apply your understanding in a knowledge check covering these concepts.