These two variables help draw the arrow-heads. Can you tell what they do?
16
式17: "l" equals 0.9 6l=0.96
negative 10−10
1010
17
式18: "a" Subscript, "l" , Baseline equals 11.2al=11.2
negative 10−10
2020
18
Now we draw the axes. x_arr and y_arr are helper functions that'll we'll use in equations 23, 24, and 25
19
式20: "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "x" Subscript, "s" , Baseline , "y" Subscript, "s" , Baseline , right parenthesis equals left brace, 0 less than "t" less than "l" : "x" Subscript, "s" , Baseline "t" , "l" less than "t" less than StartFraction, "l" plus 1 Over 2 , EndFraction : "l" "x" Subscript, "s" , Baseline plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis minus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis , StartFraction, "l" plus 1 Over 2 , EndFraction less than "t" less than 1 : "l" "x" Subscript, "s" , Baseline plus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis , right bracexarrt,xs,ys=0<t<l:xst,l<t<l+12:lxs+cos5π6xst−l−sin5π6yst−l,l+12<t<1:lxs+sin5π6yst−l+12+cos5π6xst−l+12
20
式21: "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "x" Subscript, "s" , Baseline , "y" Subscript, "s" , Baseline , right parenthesis equals left brace, 0 less than "t" less than "l" : "y" Subscript, "s" , Baseline "t" , "l" less than "t" less than StartFraction, "l" plus 1 Over 2 , EndFraction : "l" "y" Subscript, "s" , Baseline plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis plus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis , StartFraction, "l" plus 1 Over 2 , EndFraction less than "t" less than 1 : "l" "y" Subscript, "s" , Baseline minus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis , right braceyarrt,xs,ys=0<t<l:yst,l<t<l+12:lys+cos5π6yst−l+sin5π6xst−l,l+12<t<1:lys−sin5π6xst−l+12+cos5π6yst−l+12
21
式22: left parenthesis, "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "x" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "x" Subscript, "y" , Baseline , right parenthesis , "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "x" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "x" Subscript, "y" , Baseline , right parenthesis , right parenthesisxarrt,alxx,alxy,yarrt,alxx,alxy
定義域t最小値: 00
less than or equal to "t" less than or equal to≤t≤
定義域t最大値: 11
22
式23: left parenthesis, "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "y" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "y" Subscript, "y" , Baseline , right parenthesis , "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "y" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "y" Subscript, "y" , Baseline , right parenthesis , right parenthesisxarrt,alyx,alyy,yarrt,alyx,alyy
定義域t最小値: 00
less than or equal to "t" less than or equal to≤t≤
定義域t最大値: 11
23
式24: left parenthesis, "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "z" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "z" Subscript, "y" , Baseline , right parenthesis , "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "z" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "z" Subscript, "y" , Baseline , right parenthesis , right parenthesisxarrt,alzx,alzy,yarrt,alzx,alzy
定義域t最小値: 00
less than or equal to "t" less than or equal to≤t≤
定義域t最大値: 11
24
And, finally, we draw the graph in blue and green. Can you figure out what g(t) and h(t) do?
25
式26: "g" left parenthesis, "x" , right parenthesis equals 2 "s" left parenthesis, StartFraction, floor left parenthesis, "x" times left parenthesis, "n" plus 1 , right parenthesis , right parenthesis Over "n" , EndFraction minus .5 , right parenthesisgx=2sfloorx·n+1n−.5
26
式27: "h" left parenthesis, "x" , right parenthesis equals 2 "s" left parenthesis, mod left parenthesis, "x" times left parenthesis, "n" plus 1 , right parenthesis , 1 , right parenthesis minus .5 , right parenthesishx=2smodx·n+1,1−.5
27
式28: left parenthesis, "x" Subscript, "x" , Baseline "g" left parenthesis, "t" , right parenthesis plus "y" Subscript, "x" , Baseline "h" left parenthesis, "t" , right parenthesis plus "z" Subscript, "x" , Baseline "f" left parenthesis, "g" left parenthesis, "t" , right parenthesis , "h" left parenthesis, "t" , right parenthesis , right parenthesis , "x" Subscript, "y" , Baseline "g" left parenthesis, "t" , right parenthesis plus "y" Subscript, "y" , Baseline "h" left parenthesis, "t" , right parenthesis plus "z" Subscript, "y" , Baseline "f" left parenthesis, "g" left parenthesis, "t" , right parenthesis , "h" left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesisxxgt+yxht+zxfgt,ht,xygt+yyht+zyfgt,ht
定義域t最小値: 00
less than or equal to "t" less than or equal to≤t≤
定義域t最大値: 11
28
式29: left parenthesis, "x" Subscript, "x" , Baseline "h" left parenthesis, "t" , right parenthesis plus "y" Subscript, "x" , Baseline "g" left parenthesis, "t" , right parenthesis plus "z" Subscript, "x" , Baseline "f" left parenthesis, "h" left parenthesis, "t" , right parenthesis , "g" left parenthesis, "t" , right parenthesis , right parenthesis , "x" Subscript, "y" , Baseline "h" left parenthesis, "t" , right parenthesis plus "y" Subscript, "y" , Baseline "g" left parenthesis, "t" , right parenthesis plus "z" Subscript, "y" , Baseline "f" left parenthesis, "h" left parenthesis, "t" , right parenthesis , "g" left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesisxxht+yxgt+zxfht,gt,xyht+yygt+zyfht,gt
定義域t最小値: 00
less than or equal to "t" less than or equal to≤t≤
