Maxsurf has two different ways of displaying surface curvature. First, rendering of the surface can be used to display a colour shading which indicates the curvature across the surfaces. Secondly, curvature along a selected contour or contours can be displayed as a porcupine; see Curvature on Contours on page 109.
Maxsurf has four different ways of calculating and rendering curvature on a surface. You control these settings using the Rendering command from the Display menu. Before you use Rendering, make sure that you have used the Outside Arrows command to set up the surface normal direction for each of the surfaces. Render may only be selected when the Perspective window is active.
To display the rendered view, it is necessary to turn on hidden surface elimination. It is then possible to display a shaded view of the design, or to use false colouring to highlight the curvature of the surfaces.
Selecting Hidden Surface Elimination performs surface shading over the surface, using a fixed light source. If Smooth Shading is selected, the base colours of the surfaces are those chosen in the Appearance option from the Surface menu.
Shading using polygons is utilised. Surface contours may also be displayed with this option.
An alternative shading algorithm is used to provide smoother rendering. The colours of the surfaces may be changed in the Appearance dialog.
To examine the fairness of your design, Maxsurf can use false colouring to display four types of surface curvature. These have different uses and are described below:
Is the product of the maximum and minimum curvatures at a point on the surface. Gaussian curvature will indicate whether the surface is locally elliptical (positive Gaussian curvature, i.e. both curvatures in the same direction), whether it is hyperbolic (negative Gaussian curvature, curvatures with opposite signs i.e. saddle shaped), or whether it is developable (zero Gaussian curvature).
Gaussian curvature is a useful indicator of areas of twist in a surface, but is not directly linked to surface fairness. It is possible for a surface to be quite unfair and still be developable, yet the Gaussian curvature display will not reveal any problems.
Gaussian curvature can be used as an indication of whether a surface is developable. A developable surface is one that can be formed out of a flat sheet material by bending or rolling, without stretching or distorting the material. In this case, the surface will have a Gaussian curvature of zero at all points; i.e. the surface is only curved in one direction and straight in the direction orthogonal to that. See Developable Surfaces on page 95 for more information on what developable surfaces are and Modelling Developable Surfaces on page 146 for information on how to model developable surfaces in Maxsurf.
You can adjust the brightness value to make the display more or less sensitive to the Gaussian curvature values. See Brightness Level on page 107 for more information.
Note:
The Gaussian curvature gives an indication
of developability, but only should only be used to isolate areas where the
plate will be less developable.
If you want to be certain of a plates’ developability, load the surface into
Workshop and develop a surface plate. You can then examine the strain
distribution on the plate; the plate is developable if there is no strain. A
small amount of strain can be acceptable dependent on the builders’ plate
bending equipment and production techniques.
See the Workshop manual for more information, especially regarding precision
settings during plate development.
This is a display of the curvature of each longitudinal parametric curve, taken perpendicular to the surface at each point along the curve.
This display is extremely useful for determining the longitudinal fairness of a design. You should look for an even graduation of colour along the hull. Inflections can be detected by looking for changes from blue (positive curvature) to red (negative curvature). If you choose to show positive curvature values only, do so by using the following settings:
This will reveal areas of negative curvature by painting them black.
Is the curvature of each transverse parametric curve, also taken perpendicular to the surface at each point along the curve.
This display is extremely useful for determining the transverse fairness of a design. You can mask off areas of positive or negative curvature in the same way as with the longitudinal curvature display.
The convexity check highlights any areas of negative curvature.
The convexity check calculates and displays the minimum curvature for each point on the surface. If this minimum curvature is less than zero, the surface is locally concave.
The brightness level referred to in the dialog affects the way in which the colours in the display are mapped onto the curvature values.
Because the range of colours is small and the range of curvatures infinite you may need to change the colouring to suit the curves you are looking at. Changing the brightness level re-maps the colours - if the image is very dark and it is difficult to distinguish different curvatures, try using a smaller number. On the other hand if the image tends to be all pale colours, try a darker tonal value.
For Gaussian curvature, a higher brightness level will make the display more sensitive to non-zero Gaussian curvature, highlighting more areas. See Curvature Display Using Rendering on page 105 for more information.
Maxsurf allows the user to edit the lighting settings used in the perspective window when rendering is turned on.
Light Positions
Maxsurf has the option to use four different light sources. These can be turned on and off by clicking in the Render toolbar.
It is possible to vary the location of these lights by editing values in a lighting dialog. This dialog is displayed by clicking on the right most icon in the Render toolbar when the Perspective window is active and rendering is turned on.
Each light is specified by three values, distance, bearing and elevation. Distance is measured from the centre of the view in the perspective window. Bearing is taken relative to the direction from the eye to the object being viewed. For example, a light at 0 degrees is pointing in the same direction as the eye is looking at the object, 90 degrees is to the right of the object, -90 degrees is to the left of the object and 180 degrees is behind the object. Elevation is in degrees above the horizontal. A negative elevation value defines a light shining up from below the horizontal.
Light Intensities
Ambient, Diffuse and Specular values define what kind of reflection will be seen on the surface. If only ambient light values are specified, the object will be lit evenly from all directions and its reflected light will not appear to change in brightness as it is rotated. This is analogous to the sort of light seen on an overcast day. The result is no differentiation of colour or brightness across the surface.
Diffuse light is directional but is made up of parallel rays. The effect on an object illuminated with a diffuse light is that it changes in brightness as it is rotated due to the change in the incident angle of the surface.
A specular light is one that comes from a specific point such as a light bulb. When an object is lit with specular lights, definite highlights will be seen moving across the surface as it is rotated.
In practice, the ideal combination seems to be a small amount of ambient light, and roughly equal contributions from the diffuse and specular lights.
Smooth shading rendering uses OpenGL. OpenGL supports transparency and this may be specified on a surface by surface basis using the Appearances dialog in the Display menu.
OpenGL should work correctly with all versions of Microsoft Windows, except for the earliest releases of Microsoft Windows 95. These users, who are using a version of Windows 95 prior to OSR2, will need to download the OpenGL DLL. This is a free download, available from www.microsoft.com. Users should install the OpenGL drivers supplied with their video card or the default driver installed with Microsoft Windows.
OpenGL requires suitable driver software to run correctly. The driver required depends on the operating system and video card you have on your computer. The driver is normally supplied by Microsoft, or the video card or video card chipset manufacturer. Occasionally there may be problems with the driver, which prevent Maxsurf from rendering the image correctly or may even cause the computer to crash. This is more likely for very new video cards and/ or new, or less popular, operating systems such as MS Windows 2000 or MS Windows NT. This is because the drivers will have had less testing. If a problem occurs, one way of helping to determine if the driver or Maxsurf is at fault is to try running other OpenGL software such as the OpenGL screen savers; if the OpenGL screen saver crashes, the problem is probably with the OpenGL driver and you should try to update it. Video card manufacturers regularly update their drivers and these are normally available from their web sites. Another web site, which can be very helpful, is: www.opengl.org.
The second way to display curvature on a Maxsurf design is to select a contour or group of contours, and use the Show Curvature command from the Display menu. Curvature may be displayed on all surface contours except intersection lines.
To select a contour, click on the contour. It will be highlighted with a different line thickness and colour. To select more than one contour, shift-click on other contours.
When you choose Show Curvature, "Porcupines" are displayed perpendicular to the curve, and their lengths are inversely proportional to the square root of the radius of curvature at that point on the curve. Therefore the longer the porcupine line, the tighter the curve.
Note:
The value of the smallest radius (tightest bend) on a given curve is displayed numerically at the end of the porcupine located at the corresponding position on the curve.
To hide the display of curvature porcupines, choose Hide Curvature from the Display menu.
The lengths of the curvature porcupines may be scaled in the Curvature Scaling Factor field in the Preferences dialog.