Continuity and Curvature of a X-Topology Surface

The next phase of this tutorial modifies the X-Topology curves to review the different inter-patch continuities produced by the various surface patch options.

74. Select and edit the left X-Topology curve.

75. Change the Z coordinate of the middle control point to 3.0m.

76. Change the Z coordinate of the last control point to 30.0m.

The attached curves will update to the new location of the left curve and the surface should follow suit as shown below.

77. Select and edit the top curve. The coordinates of first point are shown in blue because the point references another curve. Change the Z coordinate of the middle control point to 3.0m.

The surface definition should now be based upon symmetrical control points along the diagonal.

78. Select and edit the central curve running vertically down the surface.

79. Change the Z coordinate of the middle control point to 3.0m.

The definition should now look like the image below.

80. Finished editing the curve and select the surface.

81. Change the colour of the surface to make it darker to allow the specular area of the surface shows up when it is rendered.

82. Render the surface.

83. Rendering the surface and looking how the shiny specular area moves as the view is rotated creates one way of reviewing surface fairness and continuity.

84. Continuity can be review by looking at the curvature of the surface. Change the surface so that it is viewed in wireframe mode and turn of the surface parameters, (Right-Click -> X-Topology Surface -> Show Parameters).

85. Gaussian Curvature can be used to indicate single or double curvature. It is displayed by toggling the menu items in the surface analysis area on the the Right-Click menu, (Right-Click -> X-Topology Surface -> Show Surface Analysis -> Gaussian Curvature).

The degree of curvature and its type are indicated by shading the surface in different colours.

86. Curvature can also be reviewed by displaying Zebra lines, (Right-Click -> X-Topology Surface -> Show Surface Analysis -> Zebra (Isophotes)).

Different coloured lines are produced for intervals of angles between the surface normal and a directional light source. The angle interval and light direction is control in PolyCAD Options, in the Surface Zebra Shading Parameters group. The image below shows the zebra lines produced by the default Gregory Bezier surface.

87. Select the X-Topology Surface and, in the attributes panel, change the Surface Patch Type to "Coons with Browns Twist".

The Zebra shading pattern will change to indicate a different range of continuity across the surface patches.

87. Select the X-Topology Surface and, in the attributes panel, change the Surface Patch Type to "Coons with Gregory Twist".

The Zebra pattern will change again.

88. Zooming in allows the continuity across patches to be reviewed in more detail.

89. In PolyCAD Options, displayed when no entities are being edited or are selected. In the Surface Zebra Shading Parameters group, the light source direction can be changed by rotating the stripped ball and the angle interval can be changed.

Changing the shading options will highlight the continuity across different patch edges.