[css-nav-1] Modify the definition of the distance function

css-nav-1/Overview.bs

@@ -1041,11 +1041,11 @@ Issue(w3c/csswg-drafts#2324): CSS should have a term for “border box taking in
 
 To <dfn lt="find focusable areas | finding focusable areas">find focusable areas</dfn> within a containing element <var>C</var>,
 with an optional <var>visibleOnly</var> argument that defaults to <code>true</code>,
-follow the following steps:
+run the following steps:
 
 1. Let <var>focusables</var> be the <a spec=infra for="/">set</a> of all the <a>focusable areas</a> whose [=DOM anchor=] are descendants of <var>C</var>.
     In the case of [=boxes=] with several [=box fragments=], each [=box fragment=] is considered separately.
-2. The UA should <a spec=infra for=set>remove</a> from <var>focusables</var> items that have a [=DOM anchor=] whose <a element-attr spec=html><code>tabindex</code></a> attribute is set to a negative value.
+2. The User Agent should <a spec=infra for=set>remove</a> from <var>focusables</var> items that have a [=DOM anchor=] whose <a element-attr spec=html><code>tabindex</code></a> attribute is set to a negative value.
 
     Note: This is a "SHOULD" in order to mirror the exclusion of elements with negative tabindex
     from the <a>sequential focus navigation order</a> as defined in [[HTML#the-tabindex-attribute]].
@@ -1087,7 +1087,7 @@ To <dfn lt="select the best candidate | selecting the best candidate">select the
 within a <a spec=infra for="/">set</a> of <var>candidates</var>
 in a direction <var>dir</var>,
 starting from <var>searchOrigin</var>,
-follow the following steps:
+run the following steps:
 
 1. If <var>candidates</var> is <a spec=infra for=set>empty</a>, return <code>null</code>
 2. If <var>candidates</var> contains a single item, return that item
@@ -1098,19 +1098,19 @@ follow the following steps:
 4. Let <var>insiders</var> be the subset of <var>candidates</var> items
     whose [=DOM anchor=] are descendants of <var>searchOrigin</var>
     and whose <a>boundary box</a>'s
-    * top edge is below the top edge of <var>insideArea</var> if <var>D</var> is <code>down</code>
-    * bottom edge is above the bottom edge of <var>insideArea</var> if <var>D</var> is <code>up</code>
-    * right edge is left of the right edge of <var>insideArea</var> if <var>D</var> is <code>left</code>
-    * left edge is right of the left edge of <var>insideArea</var> if <var>D</var> is <code>right</code>
+    * top edge is below the top edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/down}}
+    * bottom edge is above the bottom edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/up}}
+    * right edge is left of the right edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/left}}
+    * left edge is right of the left edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/right}}
 
     Note: this sub-setting is necessary to avoid going in the opposite direction than the one requested.
 5.
     * If <var>insiders</var> is non empty
         1. Let <var>closest subset</var> be the subset of <var>insiders</var> whose <a>boundary box</a>'s
-            * top edge is closest to the top edge of <var>insideArea</var> if <var>D</var> is <code>down</code>
-            * bottom edge is closest to the bottom edge of <var>insideArea</var> if <var>D</var> is <code>up</code>
-            * right edge is closest to the right edge of <var>insideArea</var> if <var>D</var> is <code>left</code>
-            * left edge is closest to the left edge of <var>insideArea</var> if <var>D</var> is <code>right</code>
+            * top edge is closest to the top edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/down}}
+            * bottom edge is closest to the bottom edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/up}}
+            * right edge is closest to the right edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/left}}
+            * left edge is closest to the left edge of <var>insideArea</var> if <var>dir</var> is {{SpatialNavigationDirection/right}}
         2. If <var>closest subset</var> contains a single item,
             return that item,
             else return the first item of <var>closest subset</var> in document order,
@@ -1123,38 +1123,100 @@ follow the following steps:
         1. Set <var>candidates</var> be the subset of its items
             whose <a>boundary box</a>'s geometric center is within the closed half plane
             whose boundary goes through the geometric center of the <var>searchOrigin</var>
-            and is perpendicular to <var>D</var>.
+            and is perpendicular to <var>dir</var>.
         2. For each <var>candidate</var> in <var>candidates</var>,
-            find the points <var>P1</var> inside the <a>boundary box</a> of <var>searchOrigin</var>
-            and <var>P2</var> inside the <a>boundary box</a> of <var>candidate</var>
-            that minimize the <var>distance</var> between these two points,
-            when <var>distance</var> is defined as follows:
-
-            <dl>
-              <dt><var>distance</var>:
-                <dd><var>A</var> + <var>B</var> + <var>C</var> - <var>D</var>
-
-              <dt><var>A</var>:
-                <dd>The euclidian distance between <var>P1</var> and <var>P2</var>
-
-              <dt><var>B</var>:
-                <dd>The absolute distance in the <var>dir</var> direction between <var>P1</var> and <var>P2</var>
-
-              <dt><var>C</var>:
-                <dd>The absolute distance in the direction which is orthogonal to <var>dir</var> between <var>P1</var> and <var>P2</var>
-
-              <dt><var>D</var>:
-                <dd>The square root of the area of intersection between the <a>boundary boxes</a> of <var>candidate</var> and <var>searchOrigin</var>
-            </dl>
-        3. Return the item of the <var>candidates</var> set that has the smallest <var>distance</var>.
+            1. If the <var>searchOrigin</var> is an element, then find the points <var>P1</var> inside the <a>boundary box</a> 
+                of <var>searchOrigin</var> and P2 inside the boundary box of <var>candidate</var>.
+            2. Else if the <var>searchOrigin</var> is a point, then let the point <var>P1</var> be the <var>searchOrigin</var> 
+                and find the point <var>P2</var> inside the <a>boundary box</a>.
+        3. Let <var>intersectRect</var> be an <dfn>intersecting area</dfn> between the search origin and a candidate.
+        4. Select the <var>P1</var> and <var>P2</var> that make the smallest <var>distance</var> between those two points by 
+            <a>calculating the distance</a>.        
+        5. Return the item of the <var>candidates</var> set that has the smallest <var>distance</var>.
             If several have the same distance,
             return the first one in document order,
             unless its [=boundary box=] overlaps with the [=boundary box=] of an other item at the same distance,
             and that item is higher in the CSS [=painting order=].
             In that case, return that item instead,
-            unless it too is overlapped with another higher item at the same distance, recursively.
+            unless it too is overlapped with another higher item at the same distance, recursively.    
+</div>
+
+<div algorithm="to calculate the distance">
+To <dfn lt="calculating the distance | to calculate the distance">calculate the <var>distance</var></dfn>, the function is defined as below:
+
+<pre class="prod">
+    <var>distance</var> = <var>euclidian</var> + <var>displacement</var> - <var>alignment</var> - <var>sqrt(Overlap)</var>
+</pre>
+
+The meaning of each factor in the function is as follows:
+
+<dl dfn-type="value" dfn-for="spatial-navigation-distance-function">
+    <dt><var>euclidian</var>
+    <dd>The euclidian distance between <var>P1</var> and <var>P2</var>
+
+    <dt><var>displacement</var>
+    <dd>The degree of displacement in <var>dir</var> between <var>searchOrigin</var> and <var>candidate</var>
+    <dd>Defined as <pre class="prod">(absolute distance on the axis orthogonal to <var>dir</var> + <var>orthogonalBias</var>) * <var>orthogonalWeight</var></pre>
+
+        * <var>orthogonalBias</var>
+            * If the <var>dir</var> is {{SpatialNavigationDirection/left}} or {{SpatialNavigationDirection/right}}, 
+            height of <var>searchOrigin</var> / 2
+            * Else if the <var>dir</var> is {{SpatialNavigationDirection/up}} or {{SpatialNavigationDirection/down}}, 
+            width of <var>searchOrigin</var> / 2
+
+        * <var>orthogonalWeight</var>:
+            * If the <var>dir</var> is {{SpatialNavigationDirection/left}} or {{SpatialNavigationDirection/right}}, 30
+            * Else if the <var>dir</var> is {{SpatialNavigationDirection/up}} or {{SpatialNavigationDirection/down}}, 2
+
+    <dt><var>alignment</var>
+    <dd>The degree of alignment in <var>dir</var> between <var>searchOrigin</var> and <var>candidate</var>
+    <dd>Defined as <pre class="prod"><var>alignBias</var> * <var>alignWeight</var></pre>
 
+        * <var>alignBias</var>
 
+            * If the <var>dir</var> is {{SpatialNavigationDirection/left}} or {{SpatialNavigationDirection/right}}, 
+            height of <var>intersectRect</var> / height of <var>candidate</var>
+            * Else if the <var>dir</var> is {{SpatialNavigationDirection/up}} or {{SpatialNavigationDirection/down}}, 
+            width of <var>intersectRect</var> / width of <var>candidate</var>
+
+        * <var>alignWeight</var> is 5
+
+    <dt><var>sqrt(Overlap)</var>
+    <dd>The square root of an <a>overlapping area</a> between the <a>boundary boxes</a> of <var>searchOrigin</var> and <var>candidate</var>
+    <dd>Let <var>overlapRect</var> be 
+    <var>intersectRect</var> if the <a>overlapping area</a> exists,
+    and 0 otherwise.
+    <dd>Defined as <pre class="prod">sqrt(height of <var>overlapRect</var> * width of <var>overlapRect</var>)</pre>
+</dl>
+
+NOTE: The values of <var>alignWeight</var> and <var>orthogonalWeight</var> in the function are decided based on 
+        the collected <a href="https://wicg.github.io/spatial-navigation/tests/ux/list.html">UX test cases</a>. 
+        It aims to show the generally expected result in the real pages.
+        Everyone is welcome to contribute to the test cases!
+
+<div class='example'>
+    This example shows how the <a>intersecting area</a>(<var>intersectRect</var>) is defined.
+
+    <figure>
+        <img alt="" src="images/intersecting-area-1.png" style="height: 200px;"/>
+        <figcaption>The <a>intersecting area</a> when there is the <a>overlapping area</a>.</figcaption>
+    </figure>
+
+    The figure above is the simplest case to define the <a>intersecting area</a>.
+    The <dfn>overlapping area</dfn> is the geometric overlap region between the two elements.
+    In this case, the <a>intersecting area</a> is the same as the <a>overlapping area</a> without reference to the direction of the navigation.
+
+    <figure>
+        <img alt="" src="images/intersecting-area-2.png" style="height: 200px;"/>
+        <figcaption>The <a>intersecting area</a> when the elements are aligned.</figcaption>
+    </figure>
+
+    In the case above, the search origin element and the candidate element are aligned and the requested direction is {{SpatialNavigationDirection/right}}.
+    The <a>intersecting area</a> is created with 
+    (1) The gap between two elements.
+    (2) The parts of the edges from each element which are overlapped 
+        when the right edge of the search origin element and the left edge of the candidate are projected to each other.
+</div>
 </div>
 
 <div class=cssapi>