Both surfaces curved as are present in the different applications of computer graphics and, generally, of those on synthetic image; are useful for creating complex three-dimensional models, vectorized image representation, control animations, definition for displaying text and animation paths for, guides for hair, scientific representations etc..
Curves using guides for simplified definition of complex surfaces (generally used to create different types of objects) which in turn are used in animation scenes or images for performing static. These techniques allow to obtain definition and editing, besides simplifying the modeling work, computing a number of advantages:
- The models are simpler in your description and therefore take up less memory.
- The data transfer is reduced (bandwidth to describe scenes).
- calculation models are standardized and incorporated into graphics hardware leveraging the parallel processing of GPUs, etc..
The advantages of using graphic curves based models are so numerous that we value their incorporation into the various stages of design and creation of virtual models.
NURBS versus Bezier
There are a variety of families of curves and the corresponding surfaces derived (by its generalization to a new dimension). In each of them you can find advantages and disadvantages that may determine its use in each particular application:
- Ease of use (handling) curve is an aspect that facilitates its popularization
- Fidelity or adaptation to a variety of forms the versatile and can achieve some standardization
- Cost or difficulty of calculating may limit its widespread use by platform limitations.
- Complexity or simple mathematical model
NURBS and Bezier curves are often used in graphical environments, to provide one or more advantages in the requirements set. Although not target our analysis into the mathematical aspects of the subject, added references for the interested reader.
Beyond the mathematical structure underlying these curves that would take us to study as models based on the Hermite polynomials and Bernstein and other models of this science, the designer is interested in graphic behavior and adaptability of these curves, for practical use.
How can we make non-mathematical approach a curve or supericie? With a purely graphic. Describing the visual aspects that can guide us in an intuitive and practical; reducing the complexity of his study.
Curves
The important part of a curve is the possibility of determining a line of infinite points defining just a few, whether points where the curve is obliged to spend, or points used as control elements.
In Blender we have a menu that gives access to Bezier curves and NURBS, open or closed (initially in a circle). Can add a curve similar to any object, and be edited in the form, position and orientation. In the 3D window will press the spacebar to access.
Curvas the Bezier
Bezier curves is called a system that developed to the years old 1960, for drawing technical drawings, in the aerospace and automotive design. Its name is in honor of Pierre Bezier, who devised a method of mathematical description of the curves was first used successfully in programs CAD
The main distinguishing feature of this family of curves on the NURBS incorporating Blender is to introduce the different points for their definition are definite points of the curve.
Every new item that we incorporate change the path of the curve so that it contains. The curvature depends on the position of the point, but also other control elements that we will see.
The object representation is the mode of a continuous line, transformable as other objects as aforesaid.
In edit mode representation however includes graphical elements that control the shape of the curve.
By selecting the curve and go to edit mode shows each waypoint has associated two control points arranged in principle on a tangent to the curve.
With the same methods that have been seen for selection and editing of vertices in the mesh, you can select the curve for modification.
These tangents are responsible for the “curvature” or shape of the curved line. We can prove “remove” the ends of the tangent at a point. When hooker su curvature change “push” or “attracted” to the tangent.
Generally, segment length of tangency is associated with the weight or force of attraction to the curve. Tangents long attracted more strongly than short. The curve will approach more quickly to the tangent at points with more weight.
To add a new item we should be on one end and press the key “Ctrl” and then the left button mouse.
The points on the curve can be rotated, because really what are the ends rotate its tangent. This change significantly alters the curve. The rotation be made by selecting the point and pressing “R“. moving the mouse will take the rotation to be validated by pressing the left button.
The mechanism is identical to that used to move or rotate objects and we apply the same methods of data entry.
As each object en Blender, associated menus and options exist that govern their specific parameters. The curves are no exception.
Tab “Curve And Surface” allow us to generate surfaces from curves, defining a guide curve and associating at least one other to slide over the previous.
First we complete the basic manipulation and then we introduce more complex in its application.
Curvas NURBS
NURBS (English acronym of the expression Non Uniform Rational B-splines) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. (W)
Blender incorporates open and closed NURBS. Editing and processing is performed in a similar manner to that described for Bezier curves.
The main feature that differentiates them is that the points that are used are not of the curve passing, but form a polygon which is close “saved” sides.
Technically this “In” called “tangency”. We say that curve is tangential to the sides of the polygon.
If you select the curve and had to edit mode in Blender, observe the control polygon.
The NURBS curve segment (represented in black color) is tangent to the central segment of the control polygon (amarillo).
The ends of the curve does not pass through the polygon vertices when entering the curve in the scene.
Modifying the control vertices of the polygon has associated variation in the shape of the curve;
It maintains the condition of tangency with the central segment although clearly varies address.
You can force the curve to pass through the ends, and modify various parameters that alter the shape of the curve.
To indicate for example that the start and end point are the corresponding control polygon use the button “Endpoint U” , for example.
Among the options that we are in the tab “Curve Tools” have the ability to convert the curves into polygons and backward.
We may change parameters that affect the order and the resolution of the curve, being able to generate small values polygonal.
The weight (“Weight”) affect the curvature of the curve, ahacia trend showing the most value.
By key “F” closes or opens the curve, uniting or separating the start and end points.
- Curves and surfaces in computer-aided geometric design
- What is a NURBS curve or surface
- NURBS (Wikipedia)
- Archive:Spline01.gif
Blender Tutorial
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