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You can go on and convert this to real code, but if you swap the order of steps 1 and 2, you can make life much easier: 1. For each triangle in your structure, calculate the normal vector. 2. Add this vector to the normals of the three vertices of the triangle. And after this has been done for all triangles, do the following: 3. For each vertex in your structure, normalize its normal vector.

We have just covered how to add, edit, and configure pages in detail. All the other content types are similar. They all have the same or similar actions to edit; it is just the forms and the data in them that change. Let s see what changes when you want to add an image. To add an image, select Image from the Add new drop-down menu. For this type of content, the only field that is required is the Image field, which allows you to upload the image. Click the Browse button to select the image from your hard drive. If you don t fill in the Title field and you directly click the Save button, Plone will give the item the same name it had on your local machine. It is always a good habit to enter a meaningful title and a brief description of the image. Another thing that differs from the page content type is that when you create an image, it will automatically be in the Published state, not the Private state, as it is for all the other content types (see the Publishing your Documents section later in the chapter for more details). This new rule in Plone, introduced in version 3.0, solves a problem many content creators had to face in the past: it was common to upload an image, and then insert it into a page and publish it, but forget to publish the image; the result was that anonymous users couldn t view the image when viewing the page.

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Before continuing, you should know what a normal exactly is. Put quite simply, it is the direction perpendicular to the triangle. This means that in any point of the triangle, the normal is the same. Because the normal is perpendicular to the plane of the triangle, it is also perpendicular to any vector inside the triangle. So, how can you calculate the normal vector of a single triangle You do this using a cross product, because the cross product of two vectors returns the vector perpendicular to the plane of the two vectors. In the case of your triangle, you will take two sides of the triangle as vectors. By taking their cross product, you will obtain the vector perpendicular to the triangle, as indicated by the dotted line in Figure 5-13. However, the length of this normal will be based on the angle between and the length of both sides, so afterward you need to normalize your vector to unity length.

Returns the numeric value of the operand Returns the numeric value of the operand subtracted from 0

So, you won t see the State menu on the green strip for images; but you can always change the state of this item by clicking the Contents tab of the folder containing it and using the Change state button. The image content type has an additional green tab near the Edit tab called Transform. This will take you to a panel that shows the image and a drop-down menu with some options; these will let you transform the image a bit basically to rotate it or flip it around the vertical or the horizontal axis. Click the Execute button to make the transformation effective. You can t edit images directly; instead, you can edit the image on your hard drive using a graphics program such as Adobe Photoshop or GNU Image Manipulation Program (GIMP). Once complete, clicking the Edit tab allows you to upload your new image into Plone (toggling the Replace with new image: option and uploading it again). If you do a lot of image manipulation, you can add an external editor, a tool that lets you edit images using a program without having to upload and download them (to do so, you need to install and configure your favorite external editor in Plone, but we suggest doing this only if you re a skilled developer).

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