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Corrections on text formation
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3_Marker_Training/marker_multi.md

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@@ -93,7 +93,7 @@ This tells us that the origin of marker 01 is offset +30 mm in the direction of
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Let `R[1-0]` be a 4x4 matrix where the first three rows are the values specified in configuration file, and the fourth row is the row vector `{0, 0, 0, 1}`. Then when `R[1-0]` is applied to a point vector in the marker coordinate system `p[1]`, it transforms it into a point vector expressed in the multimarker coordinate system `p[0]`, i.e. `p[0] = R[1-0] • p[1]` (where • is the normal matrix multiplication operator).
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####A Visual Explanation
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In the image below, the red arrows denote the x, y and z axes of the multimarker coordinate system, aligned with marker 0. The blue arrows denote unit vectors `n̂``, `ô` and `â`, aligned with the `x`, `y`, and `z` axes of the marker 1 coordinate system. The green arrow denotes `p`, a vector extending from the origin of the multimarker coordinate system to the origin of of the marker 1 coordinate system. The transform matrix for marker 1 can then be considered 4 column vectors expressing the projection of ```, `ô`, `â` and `p` onto `x`, `y`, and `z`.
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In the image below, the red arrows denote the x, y and z axes of the multimarker coordinate system, aligned with marker 0. The blue arrows denote unit vectors ``, `ô` and `â`, aligned with the `x`, `y`, and `z` axes of the marker 1 coordinate system. The green arrow denotes `p`, a vector extending from the origin of the multimarker coordinate system to the origin of of the marker 1 coordinate system. The transform matrix for marker 1 can then be considered 4 column vectors expressing the projection of ``, `ô`, `â` and `p` onto `x`, `y`, and `z`.
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The matrix is thus:
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<pre>
@@ -102,7 +102,7 @@ The matrix is thus:
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n[z] o[z] a[z] p[z]
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</pre>
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Compare this to the example above, and it can be seen that for marker 01 on the cube, `n̂`` is aligned with the `x` axis (no change), `ô` points completely in the direction of `-z`, and `â` points completely in the direction of `+y`.
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Compare this to the example above, and it can be seen that for marker 01 on the cube, `` is aligned with the `x` axis (no change), `ô` points completely in the direction of `-z`, and `â` points completely in the direction of `+y`.
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![Cube marker axes][Cube_marker_axes]
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