Planar projection

<h2 id="mathematical-formulation">Mathematical formulation</h2>
<p>Mathematically, planar projections are <a href="/facts/Linear_transformations/Q1PBKNVV">linear transformations</a> acting on a point in three-dimensional space 
  
    
      
        
          
            a
          
          
            x
            ,
            y
            ,
            z
          
        
      
    
    {\displaystyle \mathbf {a} _{x,y,z}}
  
 to give a point 
  
    
      
        
          
            b
          
          
            u
            ,
            v
          
        
      
    
    {\displaystyle \mathbf {b} _{u,v}}
  
 on the projection plane. These transformations consist of various <a href="/facts/Function_composition/r5Pvnmth">compositions</a> of the five transformations: <a href="/facts/Orthographic_projection/L3Cv9kYD">orthographic projection</a>, <a href="/facts/Rotation_(mathematics)/6gtkkcy0">rotation</a>, <a href="/facts/Shear_mapping/HVCYblfU">shear</a>, <a href="/facts/Translation_(geometry)/KlpWmnfX">translation</a> and <a href="/facts/Projective_transformation/wCkNzUjd">perspective</a>.
</p>
<h2 id="map-uses">Map uses</h2>
<p>It is also used in maps to show the planet Earth and other planets or objects in space. This is good for maps of close-up areas.
</p>

Planar projection open-in-new

Planar projection