Engineering ToolBox - enabled for use with the amazing FREE SketchUp 3D drawing and modeling program.

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Bezier Curve - in Equal Segments

A 4 points Bezier Curve split in a custum no. of segments with equal lengths. This tool can be useful when constructing walkable U- and L-shaped stairs

bezier curve with equal length segments

A four points Bezier curve can be expressed with the equation:

P(i) = P0 (1-i)3 + P1 3 i (1-i)2 + P2 3 i2 (1-t) + P3 i3

where the interval - i - runs from 0 to 1

Add coordinates of control points, no. of intervals and no. of segments - - and insert a segmented Bezier curve to your model. In addition to line segments small lines are added to indicate the angle between the segments. These lines can used to construct steps in a stair as indicated in the example bellow.

Note! - due to the nature of the Bezier equation the length of the segments will not be exactly equal. In general: smaller intervals increases accuracy.

This Bezier curve with equal segments don't work on Windows computers. The normal Bezier curve may be helpful.

red green blue
P0 - start point P0
P1 - control point
P2 - control point P2
P3 - end point
Insert Bezier Curve from the Points above!

Control Points from two Selected Lines?
Check here!

i - interval (0 - 1) (in the Bez. eq.)
no. of segments (split the Bez. curve)
Calculated Segments

Rotate the screen or widen the window to see full table!


Example - Construction of a L-shaped stair

Note that there are limits to the steps rise and run for a stair to be walkable. Check other stairs for more information. In addition - for a step to be walkable - the steps rise and run should be more or less constant in the "natural path" of the stair.

The "natural path" differ with persons and for persons over time - but a good aproximation to the "natural path" is the Bezier curve. This tool inserts a Bezier curve in what you define as the "natural path" - and split the curve in aprox. equal length segments. These segments can be used for the further construction of the stair.


  • draw the footprint of the staircase
    footprint staircase
  • draw the control lines for the Bezier curve
    control lines bezier stair
  • measure the coordinates of the control lines and add them to the inputs above - use the "Get control points.." feature above, or from the dialog box, or use the "Tools > Text" feature in Sketchup - as used in the example above.
  • adjust the interval parameter if required (lower value - in general higher accuracy)
  • set the numbers of steps
  • insert the Bezier curve!
    bezier curve stair
  • repeat - change the control points until you find the "natural path" you believe is the best for the stair
  • extend the small lines between the segments until they touch the walls of the staircase
  • use the push/pull tool to "lift" the areas representing the steps to their exact levels. Tip! - insert a stair with the right height and the right number of steps as a reference for the push/pull tool
    control lines bezier stair
  • customize the stair and the steps - modify step noses, details ...
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Tools - accessed from within SketchUp

NOTE!! - the "insert!" and the Tools features only works when the engineeringtoolbox exension is opened from within SketchUp. Install the extension as described in the right column - restart Sketchup and open this tool from the Sketchup Plugins menu.


undo! - redo!


change color! - of the selected object(s) - may be slow for some more complicated objects (save your model first!)


iso! - top! - front! - right! - left! - back! - bottom!

Make Component

make! - makes a component of the selected object. Note that all objects from the Engineering Toolbox are inserted as individual groups. You should transfer a group to a component sharing the same definition when there is more than one instance of the same object. Tips! Rename the object to its final name before making it a component (in outliner or with right click and entity info).

Rotate Object(s)

degrees around red, green or blue axis! (select object(s) first). Very handy for objects with curved surfaces like pipes, elbows ..

Move or Copy Object(s)

move/copy! no. copies red green blue (offset from current position
- move or copy (multiple) selected objects. Make advanced geometric constructions with multiple selections, multiple copies and the offset.
Tip! - Use "Make Component" to save space and reduce computer load when working with multiple copies.

The Knife

- inserts a "Knife" to cut in one or more objects.

insert the Knife! size of the Knife

cut! - before cut: customize the inserted Knife! The Knife is a group you can rotate, change the size of, and even add or remove objects within (example - add a function curve for an advanced cut). You can also make your own Knife by naming a group "theKnife". After insert and customizing the knife - positioning it to the object(s) where to cut - select the object(s) (must be groups) - and click cut! Afterwards - select the object(s) and remove the parts of the object(s) that you don't want.
YouTube demo of the Knife!

Move an Object to another Objects Position

move! - select two objects - then click "move" and one of the objects moves to the position and angle of the other object. Handy when moving between axis systems.

Change Insertion Point

You can change the position and angle of an inserting object by pre-selecting an existing object before Insert! The inserted object will inherit the position of the selected object. Handy when working with non-default axis.

Insert Line

red green blue - Start position
red green blue - End position

insert! - use this feature to add a reference line

Insert Horizontal Plane

insert! red (size) green (size) blue (vertical position)
- use this feature to add a horizontal reference plane

Insert Vertical Plane

insert! red (horizontal position) green (size) blue (vertical size)

insert! red (size) green (horizontal position) blue (vertical size)
- use this feature to add vertical a reference plane

Insert Box

insert! red (width) green (depth) blue (height)
- use this feature to add a box to the model

Insert external Component

insert! name url
- use this feature to add an external .skp component from the internet by adding the component url


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