In this tutorial, you will learn using the remap tool in Grasshopper and controlling a set of geometries with the Graph Mapper. In the first section a recap will be given about planes. Next, you will learn some components relating to arrays. Finally, the concept of mapping will be explained.

Curve Frames and Arrays 1/5

Horizontal and Perpendicular Frames link copied

In this first example, horizontal frames will be demonstrated. There is a difference between dividing a curve and connecting those points with a line versus creating perpendicular lines from the curves. This can be useful in creating stairs along a curve, for example.

Basic Offset method

For more information you can check the following tutorial (access through TU Delft campus):

Grasshopper Points from Curve

Using Horizontal Frames

If you want perpendicular lines to the curve, you can use the Horizontal Frames component instead. Instead of returning a point, the Horizontal Frames returns a plane, oriented in the x-direction tangent to the curve and a y-direction perpendicular to the plane. Use a Number Slider or set a number to control the number of Horizontal Frames. 

Curve

Division

Horizontal Frames

Params

Input

Number Slider

 

If the direction of the offset and the SDL do not match, you can invert one or the other by using the Negative component of the y-axis output. To complete the example, use an Offset Curve component and connect the Basecurve. The offset Distance should equal the length of the SDL line by connecting the same Number Slider. If you want to retrieve the intersection points at the offset curve, use Curve-Curve.

You can now delete or save this script for future use. We will continue with another example.

Using Perpendicular Frames

In addition to Horizontal Frames, Grasshopper also has a tool to distribute Perpendicular Frames with the Perp Frames component.

Curve

Division

Prep Frames

 

If you follow the same steps as above, you’ll see that in this case the y-direction of the plane follows the z-direction of Rhino’s world coordinate system and the x-direction is perpendicular to the curve. Notice that we connected the positive X-Axis output instead of the Y-Axis output. This ensures that the vectors are in the same direction as the offset curve.

You can now delete or save this script for future use. We will continue with another example.

Curve Frames and Arrays 2/5

Curve Array link copied

The difference between this method and the previous ones is that here we define a geometry to distribute along a curve rather than defining a point or plane to draw geometry upon or move geometry to. In this example we start with curve-geometry to be converted into a solid, but you can start with any type of geometry (point, curve, surface, brep) or even multiple geometries.

Add the BaseCurve Curve components to the canvas from the earlier step. The first component should hold the base curve. The second parameter should hold a closed curve from Rhino, for example a star. 

To create a star in Rhino:

• Type Polygon command
• Type S or click on Star
• Define the NumSides by typing N
• Type the number of sides, i.e. 5 followed by enter
• Click on the view port to define the first radius
• Click again to define the second radius

Now that you have both curves defined, we can array the shape along the curve.

• First, in Rhino, define your geometry to be arrayed along the curve. In this case, we have drawn a star-like curve and set one curve. To convert this to a solid, we use:

• Connect the StarShapedCurve into the Extrude component and connected the extrusion output into Cap Holes component. 
• For the extrusion, define the direction, in this case the z-direction by using Unit Z then define the vector distance using a Number Slider. 

• If we connect the capped Brep to the Geometry input of the Curve Array command, it will distribute the geometry along the curve by a defined Number. This can be adjusted by using a Number Slider.

You can now delete or save this script for future use. We will continue with the next tutorial.

Curve Frames and Arrays 3/5

Distance based Scaling using Remapping link copied

In this chapter, you will learn how to use the remap tool. This can be useful for example, if you want to change a parameter based on a relation to another parameter. Imagine the following situation: based on the curve we drew in the previous exercise we will extrude geometry along the curve. However, the extrusion should be larger when it is further from the start point. Furthermore, the extrusion should be at least 1 and have a maximum of 10. We will use the same base curve and star shaped curve until the of this tutorial. 

First, create a curve array of geometries along the base curve.

Now we need to find the location of the geometries, based on the curve length. First, use the Area component to find the Centroid of the geometries. After that, use the Curve Closest Point component to find the location. As you can see, the Curve Closest Point has three outputs: Point, Parameter and Distance. In our case, the Parameter output describes the location on the curve.

Remap Numbers

Below is an illustration for what remapping does the a list of numbers. In Grasshopper, remapping takes each original number and scales it according to the new target range. For example, the number 2 in the original range (0 to 4) would become 5 in the new range (0 to 10).This script remaps a set of original values (0, 1, 2, 3, and 4) to a new target range (0 to 10). By calculating the minimum (0) and maximum (4) of the original values, the script scales each value accordingly: 0 maps to 0, 1 to 2.5, 2 to 5, 3 to 7.5, and 4 to 10. 

Now we are going to use the remap approach mentioned above to create a height range for our stars. 

Now we can extrude our stars according to our remapped values! To do this, you must follow the following steps:

• Change the values to a Z-Vector by connecting the remap output to a Z-Unit vector.

• Now extrude the geometries along the base curve using the Z-Unit vector as direction.

• Cap the holes of the extrusions 

The model is now finished!

Curve Frames and Arrays 4/5

Distance-Based Scaling using Graph Mapper link copied

To control, for example, the height of the geometry according to a numeric graph, you can use the Graph Mapper function. This component can be used as an input for the Value input of the Remap Numbers component, to get for example, a sin-like shape. The Graph Mapper will create a range of numbers according to a defined graph. For this tutorial we will use the script from the previous chapter.

Take a look at this example script below. This Grasshopper script changes how a set of numbers are spread out using a custom graph and new range. At the beginning of the script, five numbers between 0 and 1 are created. Then, the Graph Mapper component is used to change the pattern of these numbers based on a custom curve (i.e. a parabola graph shown here). Finally, it scales these remapped numbers to fit within a new range from 0 to 10.

The curve can be adjusted and the distribution of the values will reflect the new curve shape. 

Now let’s edit the previous script to make it compatible with the Graph Mapper component. First, we must remove and disconnect a few components from the previous script.

• Remove the Bounds component
• Disconnect the Parameter output (Curve Closest Point) to the Value input (Remap Numbers)
• Remove the Area component
• Remove the Curve Closest Point component

Add a Range component to the canvas. Connect the Number Slider with the number of points to the Steps input. You can leave the Domain input as it is.

Finally, connect the Graph Mapper to the Value Input of the Remap Number component, and connect the Mapped values to the Factor input of the Unit-Z component. You now have an arrayed geometry along a curve. The height of the extrusions is based on a Graph Mapper!

Curve Frames and Arrays 5/5

Conclusion link copied

Congratulations on completing this tutorial! Along the way, you explored various techniques to divide and offset a curve, including the basic offset method, horizontal frames, and perpendicular frames. You also learned how to array objects along a curve using the curve array tool. Additionally, you gained an understanding of remapping values and using the Graph Mapper to manipulate the heights of arrayed objects. The possibilities with these tools are endless—so why not experiment further and see what creative designs you can come up with?

Link to Grasshopper File