Expression 15: "R" Subscript, "x" , Baseline left parenthesis, "p" , theta , right parenthesis equals left bracket, "p" left bracket, 1 , right bracket , "p" left bracket, 2 , right bracket cos theta minus "p" left bracket, 3 , right bracket sin theta , "p" left bracket, 2 , right bracket sin theta plus "p" left bracket, 3 , right bracket cos theta , right bracketRxp,θ=p1,p2cosθ−p3sinθ,p2sinθ+p3cosθ
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Expression 16: "R" Subscript, "y" , Baseline left parenthesis, "p" , theta , right parenthesis equals left bracket, "p" left bracket, 1 , right bracket cos theta plus "p" left bracket, 3 , right bracket sin theta , "p" left bracket, 2 , right bracket , negative "p" left bracket, 1 , right bracket sin theta plus "p" left bracket, 3 , right bracket cos theta , right bracketRyp,θ=p1cosθ+p3sinθ,p2,−p1sinθ+p3cosθ
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Expression 17: "R" Subscript, "z" , Baseline left parenthesis, "p" , theta , right parenthesis equals left bracket, "p" left bracket, 1 , right bracket cos theta minus "p" left bracket, 2 , right bracket sin theta , "p" left bracket, 1 , right bracket sin theta plus "p" left bracket, 2 , right bracket cos theta , "p" left bracket, 3 , right bracket , right bracketRzp,θ=p1cosθ−p2sinθ,p1sinθ+p2cosθ,p3
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Expression 18: "R" left parenthesis, "p" , "x" , "y" , "z" , right parenthesis equals "R" Subscript, "x" , Baseline left parenthesis, "R" Subscript, "y" , Baseline left parenthesis, "R" Subscript, "z" , Baseline left parenthesis, "p" , "z" , right parenthesis , "y" , right parenthesis , "x" , right parenthesisRp,x,y,z=RxRyRzp,z,y,x
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Expression 19: "l" Subscript, "i" "n" "e" , Baseline left parenthesis, "p" Subscript, "o" 1 , Baseline , "p" Subscript, "o" 2 , Baseline , right parenthesis equals "t" left parenthesis, left parenthesis, "p" Subscript, "o" 1 , Baseline . "x" , "p" Subscript, "o" 1 , Baseline . "y" , right parenthesis minus "p" Subscript, "o" 2 , Baseline , right parenthesis plus "p" Subscript, "o" 2 , Baselinelinepo1,po2=tpo1.x,po1.y−po2+po2
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Expression 20: "R" Subscript, "e" "n" "d" "e" "r" , Baseline left parenthesis, "p" , right parenthesis equals left brace, "p" Subscript, "r" "o" "j" "e" "c" "t" "i" "o" "n" , Baseline equals 1 : left parenthesis, StartFraction, "p" left bracket, 1 , right bracket minus "x" Subscript, 1 , Baseline Over tan left parenthesis, 0.5 "f" Subscript, "o" "v" , Baseline , right parenthesis left parenthesis, negative "p" left bracket, 3 , right bracket plus "z" Subscript, 1 , Baseline , right parenthesis , EndFraction , StartFraction, "p" left bracket, 2 , right bracket minus "y" Subscript, 1 , Baseline Over left parenthesis, negative "p" left bracket, 3 , right bracket plus "z" Subscript, 1 , Baseline , right parenthesis tan left parenthesis, 0.5 "f" Subscript, "o" "v" , Baseline , right parenthesis , EndFraction , right parenthesis , left parenthesis, "p" left bracket, 1 , right bracket , "p" left bracket, 2 , right bracket , right parenthesis , right braceRenderp=projection=1:p1−x1tan0.5fov−p3+z1,p2−y1−p3+z1tan0.5fov,p1,p2
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Expression 21: "e" Subscript, "r" , Baseline left parenthesis, "p" , right parenthesis equals "R" Subscript, "e" "n" "d" "e" "r" , Baseline left parenthesis, "R" left parenthesis, "p" , theta Subscript, "x" , Baseline , theta Subscript, "y" , Baseline , theta Subscript, "z" , Baseline , right parenthesis , right parenthesiserp=RenderRp,θx,θy,θz