Circular slope tile collision test (inspired by “broad-phase collision”).
1
Expression 2: "f" Subscript, "c" "s" , Baseline left parenthesis, "x" , right parenthesis equals left parenthesis, cos left parenthesis, "x" , right parenthesis , sin left parenthesis, "x" , right parenthesis , right parenthesisfcsx=cosx,sinx
2
Expression 3: "f" Subscript, "c" "s" , Baseline left parenthesis, pi plus StartFraction, pi Over 2 , EndFraction min left parenthesis, "t" , 1 , right parenthesis , right parenthesis plus left parenthesis, 1 minus max left parenthesis, 0 , "t" minus 1 , right parenthesis , 1 , right parenthesis Has graph.fcsπ+π2mint,1+1−max0,t−1,1
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
Hidden Label: "c" Subscript, "p" , Baseline equals left parenthesis, 0.4 5 , 0.1 7 7 , right parenthesis Has graph. To audio trace, press ALT+T.cp=0.45,0.177
5
Expression 6: "c" Subscript, "p" , Baseline plus "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, "t" , right parenthesis Has graph.cp+crfcst
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: tauτ
6
Expression 7: "a" equals arc tangent left parenthesis, "c" Subscript, "p" , Baseline . "y" minus 1 , "c" Subscript, "p" , Baseline . "x" minus 1 , right parenthesis equals negative 2.1 5 9 9 1 9 6 9 1 9 9a=arctancp.y−1,cp.x−1
equals=
negative 2.1 5 9 9 1 9 6 9 1 9 9−2.15991969199
7
Expression 8: "c" Subscript, "p" , Baseline plus "t" "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, "a" , right parenthesis Has graph.cp+tcrfcsa
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
8
Expression 9: left parenthesis, 1 minus "c" Subscript, "r" , Baseline , right parenthesis "f" Subscript, "c" "s" , Baseline left parenthesis, pi plus StartFraction, pi Over 2 , EndFraction "t" , right parenthesis plus left parenthesis, 1 , 1 , right parenthesis Has graph.1−crfcsπ+π2t+1,1
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
9
Expression 10: "d" equals StartRoot, left parenthesis, "c" Subscript, "p" , Baseline . "x" minus 1 , right parenthesis squared plus left parenthesis, "c" Subscript, "p" , Baseline . "y" minus 1 , right parenthesis squared , EndRoot equals 0.9 8 9 8 6 3 1 2 1 8 5 1d=cp.x−12+cp.y−12
equals=
0.9 8 9 8 6 3 1 2 1 8 5 10.989863121851
10
Expression 11: left parenthesis, left parenthesis, 1 , 1 , right parenthesis plus min left parenthesis, "d" , 1 minus "c" Subscript, "r" , Baseline , right parenthesis "f" Subscript, "c" "s" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis plus "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, "t" , right parenthesis left brace, 0 less than or equal to "c" Subscript, "p" , Baseline . "x" less than or equal to 1 , right brace left brace, 0 less than or equal to "c" Subscript, "p" , Baseline . "y" less than or equal to 1 , right brace Has graph.1,1+mind,1−crfcsa+crfcst0≤cp.x≤10≤cp.y≤1
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: tauτ
11
Expression 12: left bracket, "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, pi "t" , right parenthesis plus left parenthesis, 0 , 1 , right parenthesis , "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, pi "t" minus StartFraction, pi Over 2 , EndFraction , right parenthesis plus left parenthesis, 1 , 0 , right parenthesis , left parenthesis, "t" , negative "c" Subscript, "r" , Baseline , right parenthesis , left parenthesis, negative "c" Subscript, "r" , Baseline , "t" , right parenthesis , "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, pi plus StartFraction, pi Over 2 , EndFraction "t" , right parenthesis , right bracket Has graph.crfcsπt+0,1,crfcsπt−π2+1,0,t,−cr,−cr,t,crfcsπ+π2t
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
12
Hidden Label: left bracket, "c" Subscript, "p" , Baseline plus "t" "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, arctan left parenthesis, negative "c" Subscript, "p" , Baseline . "y" , 1 minus "c" Subscript, "p" , Baseline . "x" , right parenthesis , right parenthesis left brace, "c" Subscript, "p" , Baseline . "x" greater than or equal to 1 , right brace , "c" Subscript, "p" , Baseline plus "t" "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, arctan left parenthesis, 1 minus "c" Subscript, "p" , Baseline . "y" , negative "c" Subscript, "p" , Baseline . "x" , right parenthesis , right parenthesis left brace, "c" Subscript, "p" , Baseline . "y" greater than or equal to 1 , right brace , "c" Subscript, "p" , Baseline plus "t" "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, arctan left parenthesis, negative "c" Subscript, "p" , Baseline . "y" , negative "c" Subscript, "p" , Baseline . "x" , right parenthesis , right parenthesis left brace, "c" Subscript, "p" , Baseline . "x" less than 0 , right brace left brace, "c" Subscript, "p" , Baseline . "y" less than 0 , right brace , right bracket equals a list of points. 3 items Has graph. To audio trace, press ALT+T.cp+tcrfcsarctan−cp.y,1−cp.xcp.x≥1,cp+tcrfcsarctan1−cp.y,−cp.xcp.y≥1,cp+tcrfcsarctan−cp.y,−cp.xcp.x<0cp.y<0
equals=
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13
Hidden Label: left bracket, left parenthesis, 1 , 0 , right parenthesis minus "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, arctan left parenthesis, negative "c" Subscript, "p" , Baseline . "y" , 1 minus "c" Subscript, "p" , Baseline . "x" , right parenthesis , right parenthesis left brace, "c" Subscript, "p" , Baseline . "x" greater than or equal to 1 , right brace , left parenthesis, 0 , 1 , right parenthesis minus "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, arctan left parenthesis, 1 minus "c" Subscript, "p" , Baseline . "y" , negative "c" Subscript, "p" , Baseline . "x" , right parenthesis , right parenthesis left brace, "c" Subscript, "p" , Baseline . "y" greater than or equal to 1 , right brace , negative "c" Subscript, "r" , Baseline "f" Subscript, "c" "s" , Baseline left parenthesis, arctan left parenthesis, negative "c" Subscript, "p" , Baseline . "y" , negative "c" Subscript, "p" , Baseline . "x" , right parenthesis , right parenthesis left brace, "c" Subscript, "p" , Baseline . "x" less than 0 , right brace left brace, "c" Subscript, "p" , Baseline . "y" less than 0 , right brace , left parenthesis, "c" Subscript, "p" , Baseline . "x" , negative "c" Subscript, "r" , Baseline , right parenthesis left brace, "c" Subscript, "p" , Baseline . "y" less than or equal to 0 , right brace left brace, 0 less than or equal to "c" Subscript, "p" , Baseline . "x" less than or equal to 1 , right brace , left parenthesis, negative "c" Subscript, "r" , Baseline , "c" Subscript, "p" , Baseline . "y" , right parenthesis left brace, 0 less than or equal to "c" Subscript, "p" , Baseline . "y" less than or equal to 1 , right brace left brace, "c" Subscript, "p" , Baseline . "x" less than or equal to 0 , right brace , right bracket equals a list of points. 5 items Has graph. To audio trace, press ALT+T.1,0−crfcsarctan−cp.y,1−cp.xcp.x≥1,0,1−crfcsarctan1−cp.y,−cp.xcp.y≥1,−crfcsarctan−cp.y,−cp.xcp.x<0cp.y<0,cp.x,−crcp.y≤00≤cp.x≤1,−cr,cp.y0≤cp.y≤1cp.x≤0
equals=
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5 element list
14
Expression 15: min left parenthesis, StartRoot, left parenthesis, "x" minus 1 , right parenthesis squared plus "y" squared , EndRoot , StartRoot, "x" squared plus left parenthesis, "y" minus 1 , right parenthesis squared , EndRoot , StartRoot, "x" squared plus "y" squared , EndRoot , left brace, 0 less than or equal to "y" less than or equal to 1 : abs left parenthesis, "x" , right parenthesis , 1 , right brace , left brace, 0 less than or equal to "x" less than or equal to 1 : abs left parenthesis, "y" , right parenthesis , 1 , right brace , left brace, max left parenthesis, min left parenthesis, "x" , "y" , right parenthesis , max left parenthesis, 2abs left parenthesis, "x" minus .5 , right parenthesis , 2abs left parenthesis, "y" minus .5 , right parenthesis , right parenthesis , right parenthesis less than or equal to 1 : 1 minus StartRoot, left parenthesis, "x" minus 1 , right parenthesis squared plus left parenthesis, "y" minus 1 , right parenthesis squared , EndRoot , 1 , right brace , right parenthesis less than or equal to "c" Subscript, "r" , Baseline Has graph.minx−12+y2,x2+y−12,x2+y2,0≤y≤1:absx,1,0≤x≤1:absy,1,maxminx,y,max2absx−.5,2absy−.5≤1:1−x−12+y−12,1≤cr
15
Normalizing instead of using atan2 and cossin:
16
Hidden Label: left parenthesis, 1 minus "c" Subscript, "r" , Baseline , right parenthesis StartFraction, "c" Subscript, "p" , Baseline minus left parenthesis, 1 , 1 , right parenthesis Over "d" , EndFraction plus left parenthesis, 1 , 1 , right parenthesis equals left parenthesis, 0.5 1 6 5 9 9 8 3 1 3 9 3 , 0.2 7 6 6 5 7 5 6 5 8 8 5 , right parenthesis Has graph. To audio trace, press ALT+T.1−crcp−1,1d+1,1
Expression 18: left parenthesis, max left parenthesis, 0 , 1 minus "t" , right parenthesis , min left parenthesis, "t" , 2 minus "t" , right parenthesis , right parenthesismax0,1−t,mint,2−t
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 22
18
Expression 19: left parenthesis, 1 plus StartRoot, 2 , EndRoot "c" Subscript, "r" , Baseline , right parenthesis minus "x" left brace, 0 less than or equal to "x" less than or equal to 1 plus StartRoot, 2 , EndRoot "c" Subscript, "r" , Baseline , right brace Has graph. To audio trace, press ALT+T.1+2cr−x0≤x≤1+2cr
19
Expression 20: left parenthesis, left parenthesis, 1 , 1 , right parenthesis plus min left parenthesis, "d" , 1 minus "c" Subscript, "r" , Baseline , right parenthesis "f" Subscript, "c" "s" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis plus "t" left parenthesis, "c" Subscript, "r" , Baseline plus max left parenthesis, "d" minus left parenthesis, 1 minus "c" Subscript, "r" , Baseline , right parenthesis , 0 , right parenthesis , right parenthesis "f" Subscript, "c" "s" , Baseline left parenthesis, "a" plus StartFraction, pi Over 2 , EndFraction , right parenthesis left brace, 0 less than or equal to "c" Subscript, "p" , Baseline . "x" less than or equal to 1 , right brace left brace, 0 less than or equal to "c" Subscript, "p" , Baseline . "y" less than or equal to 1 , right brace Has graph.1,1+mind,1−crfcsa+tcr+maxd−1−cr,0fcsa+π20≤cp.x≤10≤cp.y≤1
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
20
Expression 21: left bracket, "t" "c" Subscript, "p" , Baseline , left parenthesis, 1 , 1 , right parenthesis minus "t" times left parenthesis, 1 minus "c" Subscript, "p" , Baseline . "x" , 1 minus "c" Subscript, "p" , Baseline . "y" , right parenthesis , right bracket Has graph.tcp,1,1−t·1−cp.x,1−cp.y
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
21
Hidden Label: left parenthesis, 1 , 1 , right parenthesis Has graph. To audio trace, press ALT+T.1,1
