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The problem we need to solve is how to deal with the corners. In fact, it s the same problem we needed solve when working out how to deal with the corners in collisions between circles and lines in 3. It means that to solve a collision between a circle and a square, you need to break it into two parts: When the circle is closer to the sides of the square than it is to the corners, it becomes a rectangle-versus-rectangle collision problem. When the circle is closer to any of the corners than it is to the sides, it becomes a circleversus-particle collision problem. The x and y coordinates of the square s corners are the particles. To know when to use which collision strategy is just a matter of logic, and this is not at all hard to work out. You just need to find out which region of space (Voronoi region) the circle occupies, and apply the correct collision strategy for that region. Figure 4-38 illustrates where these regions are and which strategy to use for each.

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Listing 11-1. Definition of the AverageUnitPrice() function in the model <Function Name="AverageUnitPrice" ReturnType="Edm.Decimal"> <Parameter Name="category" Type="EFRecipesModel.Category" /> <DefiningExpression> ANYELEMENT(Select VALUE Avg(p.UnitPrice) from EFRecipesEntities.Products as p where p.Category == category group by p.Category.CategoryName ) </DefiningExpression> </Function> Listing 11-2. Inserting and querying the model using the model defined function AverageUnitPrice() class Program { static void Main(string[] args) { RunExample(); } static void RunExample() { using (var context = new EFRecipesEntities()) { var c1 = new Category { CategoryName = "Backpacking Tents" }; new Product { ProductName = "Hooligan", UnitPrice = 89.99M, Category = c1 }; new Product { ProductName = "Kraz", UnitPrice = 99.99M, Category = c1 }; new Product { ProductName = "Sundome", UnitPrice = 49.99M, Category = c1 }; context.Categories.AddObject(c1); var c2 = new Category { CategoryName = "Family Tents" }; new Product { ProductName = "Evanston", UnitPrice = 169.99M, Category = c2 }; new Product { ProductName = "Montana", UnitPrice = 149.99M, Category = c2 }; context.Categories.AddObject(c2); context.SaveChanges();

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Figure 4-38. Choose the collision strategy based on which region the circle occupies. You can figure out which region the circle is in by comparing its center position to the square s position, plus its half height and half width. When the circle is in a rectangle-versus-rectangle region, it literally becomes a square for collision purposes, as shown in Figure 4-39. It might look like a circle on the stage, but the collision code sees it as a square.

} // with eSQL using (var context = new EFRecipesEntities()) { Console.WriteLine("Using eSQL for the query..."); Console.WriteLine(); string sql = @"Select c.CategoryName, EFRecipesModel .AverageUnitPrice(c) as AveragePrice from EFRecipesEntities.Categories as c"; var cats = context.CreateQuery<DbDataRecord>(sql); foreach (var cat in cats) { Console.WriteLine("Category '{0}' has an average price of {1}", cat[0], ((decimal)cat[1]).ToString("C")); } } // with LINQ using (var context = new EFRecipesEntities()) { Console.WriteLine(); Console.WriteLine("Using LINQ for the query..."); Console.WriteLine(); var cats = from c in context.Categories select new { Name = c.CategoryName, AveragePrice = MyFunctions.AverageUnitPrice(c) }; foreach (var cat in cats) { Console.WriteLine("Category '{0}' has an average price of {1}", cat.Name, cat.AveragePrice.ToString("C")); } } } } public class MyFunctions { [EdmFunction("EFRecipesModel", "AverageUnitPrice")] public static decimal AverageUnitPrice(Category category) { throw new NotSupportedException("Direct calls are not supported!"); } } The following is the output from the code in Listing 11-2: Using eSQL for the query...

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Figure 4-39. The collision code treats the circle like a square when it s in a rectangle-versusrectangle region. When the circle is in a circle-versus-particle region, it completely ignores the square shape and just checks for a collision with the square s closest corner point, as shown in Figure 4-40. This is the same circle-versus-particle collision strategy we looked at in 3.

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