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author | Erich Eckner <git@eckner.net> | 2019-10-22 13:30:03 +0200 |
---|---|---|
committer | Erich Eckner <git@eckner.net> | 2019-10-22 13:30:03 +0200 |
commit | 5c0917fa2c6e16e4872c71e4e3aa545dd3f24a32 (patch) | |
tree | 0b488236cea3fdf8656378aaf4d1f35d7e03db2e | |
parent | 79c77a67e196a94197d0f8630c2d6e42212a0326 (diff) | |
download | epost-5c0917fa2c6e16e4872c71e4e3aa545dd3f24a32.tar.xz |
Radon.nb
-rw-r--r-- | Radon.nb | 9309 |
1 files changed, 8318 insertions, 991 deletions
@@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 66387, 1215] -NotebookOptionsPosition[ 65669, 1196] -NotebookOutlinePosition[ 66004, 1211] -CellTagsIndexPosition[ 65961, 1208] +NotebookDataLength[ 511114, 8544] +NotebookOptionsPosition[ 510198, 8523] +NotebookOutlinePosition[ 510533, 8538] +CellTagsIndexPosition[ 510490, 8535] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -31,35 +31,40 @@ Cell[BoxData[{ RowBox[{"s", "=", "20"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ + RowBox[{"n", "[", "x_", "]"}], ":=", + RowBox[{"Block", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"ma", ",", "mi"}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"ma", "=", + RowBox[{"Max", "@", "x"}]}], ";", "\[IndentingNewLine]", + RowBox[{"mi", "=", + RowBox[{"Min", "@", "x"}]}], ";", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"(", + RowBox[{"x", "-", "mi"}], ")"}], "/", + RowBox[{"(", + RowBox[{"ma", "-", "mi"}], ")"}]}]}]}], "\[IndentingNewLine]", + "]"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ RowBox[{"data", "[", RowBox[{"a_", ",", "\[Alpha]_", ",", "b_"}], "]"}], ":=", RowBox[{"Table", "[", RowBox[{ - RowBox[{"1.", "/", - RowBox[{"(", - RowBox[{"1", "+", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"i", "\[Equal]", "5"}], "&&", + RowBox[{"j", "\[Equal]", "5"}]}], ",", "1", ",", + RowBox[{"If", "[", RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"{", - RowBox[{"i", ",", "j"}], "}"}], ".", - RowBox[{"RotationMatrix", "[", "\[Alpha]", "]"}]}], "-", "a"}], - ")"}], ".", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"b", ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ".", - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"RotationMatrix", "[", - RowBox[{"-", "\[Alpha]"}], "]"}], ".", - RowBox[{"{", - RowBox[{"i", ",", "j"}], "}"}]}], "-", "a"}], ")"}]}]}], ")"}]}], - ",", + RowBox[{ + RowBox[{"i", "\[Equal]", + RowBox[{"-", "2"}]}], "&&", + RowBox[{"j", "\[Equal]", "2"}]}], ",", "1", ",", "0"}], "]"}]}], + "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"-", "s"}], ",", "s"}], "}"}], ",", @@ -77,6 +82,13 @@ Cell[BoxData[{ ";"}], "\[IndentingNewLine]", RowBox[{"Image", "[", "d", "]"}], "\[IndentingNewLine]", RowBox[{ + RowBox[{"mf", "=", + RowBox[{"ImageData", "@", + RowBox[{"Radon", "@", + RowBox[{"Image", "@", "d"}]}]}]}], ";"}], "\[IndentingNewLine]", + RowBox[{"Image", "@", + RowBox[{"n", "@", "mf"}]}], "\[IndentingNewLine]", + RowBox[{ RowBox[{"fd", "=", RowBox[{"Fourier", "[", "d", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ @@ -84,12 +96,13 @@ Cell[BoxData[{ RowBox[{"Max", "@", RowBox[{"Abs", "@", "fd"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Image", "@", - RowBox[{"Map", "[", - RowBox[{ + RowBox[{"n", "@", + RowBox[{"Map", "[", RowBox[{ RowBox[{ - RowBox[{"Abs", "[", "#", "]"}], "/", "mfd"}], "&"}], ",", "fd", ",", - RowBox[{"{", "2", "}"}]}], "]"}]}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Abs", "[", "#", "]"}], "/", "mfd"}], "&"}], ",", "fd", ",", + RowBox[{"{", "2", "}"}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fdi", "[", @@ -97,8 +110,10 @@ Cell[BoxData[{ RowBox[{"Block", "[", RowBox[{ RowBox[{"{", - RowBox[{"xi", ",", "yi", ",", "xip", ",", "yip", ",", "xf", ",", "yf"}], - "}"}], ",", "\[IndentingNewLine]", + RowBox[{ + "xi", ",", "yi", ",", "xip", ",", "yip", ",", "xf", ",", "yf", ",", + "xin", ",", "xipn", ",", "yin", ",", "yipn"}], "}"}], ",", + "\[IndentingNewLine]", RowBox[{ RowBox[{"xi", "=", RowBox[{"Floor", "@", "x"}]}], ";", "\[IndentingNewLine]", @@ -108,6 +123,32 @@ Cell[BoxData[{ RowBox[{"x", "-", "xi"}]}], ";", "\[IndentingNewLine]", RowBox[{"yf", "=", RowBox[{"y", "-", "yi"}]}], ";", "\[IndentingNewLine]", + RowBox[{"xin", "=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Abs", "[", "xi", "]"}], "\[LessEqual]", "s"}], ",", "1", + ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"yin", "=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Abs", "[", "yi", "]"}], "\[LessEqual]", "s"}], ",", "1", + ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"xipn", "=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Abs", "[", + RowBox[{"xi", "+", "1"}], "]"}], "\[LessEqual]", "s"}], ",", "1", + ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"yipn", "=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Abs", "[", + RowBox[{"yi", "+", "1"}], "]"}], "\[LessEqual]", "s"}], ",", "1", + ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"xi", "=", RowBox[{"Mod", "[", RowBox[{"xi", ",", @@ -136,30 +177,48 @@ Cell[BoxData[{ "\[IndentingNewLine]", RowBox[{ RowBox[{ - RowBox[{"fd", "[", - RowBox[{"[", - RowBox[{"yi", ",", "xi"}], "]"}], "]"}], "*", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"xin", "*", "yin"}], "\[Equal]", "1"}], ",", + RowBox[{"fd", "[", + RowBox[{"[", + RowBox[{"yi", ",", "xi"}], "]"}], "]"}], ",", "0"}], "]"}], "*", RowBox[{"(", RowBox[{"1", "-", "xf"}], ")"}], "*", RowBox[{"(", RowBox[{"1", "-", "yf"}], ")"}]}], "\[IndentingNewLine]", "+", RowBox[{ - RowBox[{"fd", "[", - RowBox[{"[", - RowBox[{"yip", ",", "xi"}], "]"}], "]"}], "*", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"xin", "*", "yipn"}], "\[Equal]", "1"}], ",", + RowBox[{"fd", "[", + RowBox[{"[", + RowBox[{"yip", ",", "xi"}], "]"}], "]"}], ",", "0"}], "]"}], "*", + RowBox[{"(", RowBox[{"1", "-", "xf"}], ")"}], "*", "yf"}], "\[IndentingNewLine]", "+", RowBox[{ - RowBox[{"fd", "[", - RowBox[{"[", - RowBox[{"yi", ",", "xip"}], "]"}], "]"}], "*", "xf", "*", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"xipn", "*", "yin"}], "\[Equal]", "1"}], ",", + RowBox[{"fd", "[", + RowBox[{"[", + RowBox[{"yi", ",", "xip"}], "]"}], "]"}], ",", "0"}], "]"}], "*", + "xf", "*", RowBox[{"(", RowBox[{"1", "-", "yf"}], ")"}]}], "\[IndentingNewLine]", "+", RowBox[{ - RowBox[{"fd", "[", - RowBox[{"[", - RowBox[{"yip", ",", "xip"}], "]"}], "]"}], "*", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"xipn", "*", "yipn"}], "\[Equal]", "1"}], ",", + RowBox[{"fd", "[", + RowBox[{"[", + RowBox[{"yip", ",", "xip"}], "]"}], "]"}], ",", "0"}], "]"}], "*", RowBox[{"-", "xf"}], "*", "yf"}]}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ @@ -174,14 +233,26 @@ Cell[BoxData[{ RowBox[{"Sin", "@", "\[Beta]"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"r", ",", - RowBox[{"-", "s"}], ",", "s"}], "}"}], ",", + RowBox[{ + RowBox[{"-", "2"}], "s"}], ",", + RowBox[{"2", "s"}]}], "}"}], ",", RowBox[{"{", - RowBox[{"\[Beta]", ",", "0", ",", "\[Pi]", ",", "0.1"}], "}"}]}], + RowBox[{"\[Beta]", ",", "0", ",", "\[Pi]", ",", "0.02"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Image", "@", - RowBox[{"Map", "[", - RowBox[{"Abs", ",", "fr", ",", - RowBox[{"{", "2", "}"}]}], "]"}]}], "\[IndentingNewLine]", + RowBox[{"n", "@", + RowBox[{"Map", "[", + RowBox[{"Abs", ",", "fr", ",", + RowBox[{"{", "2", "}"}]}], "]"}]}]}], "\[IndentingNewLine]", + RowBox[{"Image", "@", + RowBox[{"n", "@", + RowBox[{"Map", "[", + RowBox[{"Abs", ",", + RowBox[{"Transpose", "@", + RowBox[{"Map", "[", + RowBox[{"Fourier", ",", + RowBox[{"Transpose", "@", "mf"}]}], "]"}]}], ",", + RowBox[{"{", "2", "}"}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r", "=", RowBox[{"Transpose", "@", @@ -190,303 +261,36 @@ Cell[BoxData[{ RowBox[{"Transpose", "@", "fr"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Image", "@", - RowBox[{"Map", "[", - RowBox[{"Abs", ",", "r", ",", - RowBox[{"{", "2", "}"}]}], "]"}]}]}], "Input", + RowBox[{"n", "@", + RowBox[{"Map", "[", + RowBox[{ + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Re", "@", "#"}], ",", + RowBox[{"Im", "@", "#"}], ",", + RowBox[{"Abs", "@", "#"}]}], "}"}], "&"}], ",", "r", ",", + RowBox[{"{", "2", "}"}]}], "]"}]}]}]}], "Input", CellChangeTimes->{{3.7806544496501417`*^9, 3.780654669416645*^9}, { 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