OBD:PLEA: Difference between revisions

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 {{OBDtr| 0x00 | res_id   |FF0000| 01 41 02 00 | 577   | 00577-.PLEA }}
 {{OBDtr| 0x04 | lev_id   |FFFF00| 01 00 00 06 | 3     | level 3 }}
-{{OBDtr| 0x08 | char[20] |00FF00| AD DE       | dead  | unused }}
+{{OBDtr| 0x08 | char[20] |00FF00| AD DE       | dead  | padding }}
-{{OBDtr| 0x1C | int32    |00FFFF| 03 00 00 00 | 13554 | array size }}
+{{OBDtr| 0x1C | uint32    |00FFFF| 03 00 00 00 | 13554 | array size }}
 {{OBDtrBK}}
 {{OBDtr| 0x00 | float    |FFC8C8| 00 00 00 00 | 0.000000 | 'a' coefficient of the plane equation (x component of plane's normal) }}
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 ;Plane equation
-:The canonical equation for a [http://mathworld.wolfram.com/Plane.html plane] in 3D is :
+:The canonical equation for a [https://mathworld.wolfram.com/Plane.html plane] in 3D is
-::a * x + b * y + c * z + d = 0
+::'''a * x + b * y + c * z + d = 0,'''
-:where (a, b, c, d) are 4 real numbers. The plane is the set of points (x, y, z) verifying that equation.
+:with (a, b, c, d) being 4 real numbers and (a, b, c) forming a nonzero vector (the plane's "normal").
-:The four floats in one of a PLEA's packages are exactly the (a, b, c, d) of the above definition.
+:*The set of points (x, y, z) verifying '''a * x + b * y + c * z + d = 0''' are said to be in the plane or at the plane.
-::In that case, the first package of the above example defines the plane (0 * x + 0 * y + 1 * z + 612 = 0), i.e., the vertical plane z = -612.
+:*The set of points (x, y, z) verifying '''a * x + b * y + c * z + d > 0''' are said to be in front of the plane.
-Planes are used for environment culling, collision detection and [[wikipedia:Binary_space_partitioning|BSP]].
+:*The set of points (x, y, z) verifying '''a * x + b * y + c * z + d < 0''' are said to be behind the plane.
+:'''N.B.''' If a=b=c=0, then the equation is degenerate and applies either to the whole space (if d=0) or to no points at all (if d is non-zero).
+:As a further convention, if (a,b,c) is normalized at unit length (i.e., '''a*a + b*b + c*c = 1''') then d is the distance from the plane to the world's origin, along the normal vector.
+:The four floats in each element of a PLEA are exactly the (a, b, c, d) of the above definition.
+:In the above example, the first element defines the plane (0 * x + 0 * y + 1 * z + 612 = 0), i.e., the vertical plane z = -612.
+;What planes are for and how they are referenced
+:Planes are used for environment culling, collision detection and [[wikipedia:Binary_space_partitioning|BSP]].
+:The plane equations stored in PLEA are referenced from such data as [[ABNA]], [[AKBP]], [[AKBA]] and [[AGQC]] by means of a 32-bit array index.
+:However, the high bit of those 32-bit references is not part of the array index, instead it indicates whether the facing of the plane should be flipped.
+:*If the high bit is not set, then the 4 values (a, b, c, d) are used as described above.<br />(If referencing the above example without a high bit, then any points with z > - 612 will be in front of the plane, whereas points with z < -612 will be behind the plane.)
+:*If the high bit is set, then the plane equation coefficients become (-a, -b, -c, -d).<br />(If referencing the above example with a high bit, then any point with z > - 612 will be behind the plane, whereas points with z < -612 will be in front of the plane.)
+:This means that the actual array index is a 31-bit value (i.e., there can "only" be up to 2,147,483,648 distinct planes in a level), but the same array element can be used for two different facing directions.
 {{OBD_File_Footer | type=PLEA | prev=OTLF | next=PNTA | name=Plane Equation Array | family=Level}}
+{{OBD}}