Object Properties
Use this option to determine the type of roll-off curve.
Parameters of a Cycloid
The Cycloid is a rolling curve of a circle (radius R) along a straight line.
The Epicycloid is a rolling curve of a circle (radius r) that moves outside a second (usually) larger circle (radius R).
Parameters of an Epicycloid
The Hypocycloid is a rolling curve of a circle (radius r) that moves within a second (usually) larger circle (radius R).
Parameters of a Hypocycloid
With the ordinary Cycloid (a = R), the observed point P (which forms the curve) is located on the radius of the circle. With the shortened Cycloid (a \ R) outside.
: Different R-to-a ratios. End Angle 360° at the top and 720° at the bottom.
In the ordinary Epicycloid, the observed point P (which forms the curve) is located on the radius of the inner circle (a = r). In the shortened Epicycloid, it is located within the inner circle (a \ r).
The following illustration shows some of the possible curves.
Various picycloids
Special cases, known as Pascals snails, arise when the radii of the two circles are equal. If the point P is also located on the radius of the outer circle (a = r), the so-called Cardoid is created. (illustration on the right).
Epicycloids as Pascals snails.
In the ordinary Hypocycloid, the observed point P (which forms the curve) is located on the radius of the inner circle (a = r). In the shortened Hypocycloid, it is located within the inner circle (a \ r).
If the radius of the outer circle is exactly four times that of the inner circle, the so-called Astroids are obtained. (top right image).
The following illustrations show some of the possible curves. You will find the selected values under each illustration.
Various Hypocycloids.
These values define the start and end positions of the rolling circle. There is a small, but crucial, difference between the Cycloid, Hypocycloid and Epicycloid values.
For the Cycloid, enter the Start and End Angles of the rolling circle here.
With Epicycloid and Hypocycloid, you define the values for the start and end points on the fixed circle. However, the rolling circle still starts at 0°. Simply consider this angle range as the range in which the roll curve becomes visible.
Angle range left 0 - 360°, right 90 - 270°
Here you can define the layer on which the spline should come to rest.
Enabling this option will reverse the point order of the spline (see also Spline Primitives.
Here you set how the spline is to be subdivided during further processing. This is always important when you generate meshes with the help of generators. Depending on which type you select from the menu for Interpolation, you have further options.
This type of interpolation uses the interpolation points of the spline directly and connects them via straight lines without setting additional intermediate points.
You cannot make entries in the fields for Points or Angle.
This type of interpolation divides the spline in such a way that a corresponding number of Points are used per interpolation point. The inserted points follow the natural course of the spline directly, i.e. they are closer together at support points than in between. The curve resulting from this interpolation does not necessarily pass through the interpolation points. If a spline has several segments, the value for Points applies to each interpolation point of each segment.
You cannot make any entries in the Angle field.
This interpolation type divides the spline so that the selected number of Points is used for each interpolation point. The points are exactly the same distance apart. The curve resulting from this interpolation does not necessarily pass through the interpolation points. If a spline has several segments, the value for Points applies to each interpolation point of each segment.
You cannot make any entries in the Angle field.
Opened spline: ((Points + 1) * (number_of_base_points - 1)) +1
Closed spline: (Points + 1) * number_of_base_points
This means, for example, that an open spline with four support points and a Points value of 2 is divided into a total of ((2+1)*(4-1))+1 = 10 points. If you close this spline, (2+1)*4 = 12 points are used. This procedure prevents, for example, a spline from being split more roughly after it has been closed.
This type of interpolation always sets intermediate points if the angular deviation of the curve is greater than the value entered under Angle. The curve resulting from this interpolation passes exactly through the interpolation points. If a spline has several segments, the value for Angle applies to each segment.
In contrast to the other interpolation types, different interpolations result if you change the interpolation point sequence of the spline.
The subdivision, also known as Adaptive, produces the best results in rendering. This is therefore the default Interpolation method.
You cannot make any entries in the Points field.
Subdivided is similar to the Adaptive type. In addition, intermediate points are inserted until the segments in between are shorter than the length defined under Max Length. This does not necessarily mean that the point distances correspond exactly to Max Length. Smaller values lead to higher quality, but as is so often the case, they also have the disadvantages associated with high point counts (slower redraw speed in the editor, etc.).
This enables significantly better rendering quality, especially with deformed text. If you enter the same value for Max Length as for Size in the Extrude object (Caps tab, Regular Grid option activated), you will get fairly perfect cap areas and edges without shading errors, as the subdivisions of letters and their caps fit together and triangles do not have to be inserted arbitrarily to connect the two mesh elements.
On the left Adaptive, on the right Subdivided Interpolation in combination with a Formula deformation object. Note the clearly defined edges on the right-hand side of the illustration.
This parameter, which is only effective in Subdivided Interpolation mode, controls the maximum spline segment length without an intermediate point (see above for Subdivided) must be inserted.