PC Shareware 2000 January/PCShareware-1-00.iso/s3d/SIMPLY3D/DOCS/TUTOR6.DP

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Tutorial 6: Working With Lights
Completion time 45 minutes
tMBefore a view can be rendered, light resources must be defined and positioned
*2Oin that view.  In this tutorial we will explore the methods by which lights are
created and positioned.
*A In this tutorial you will learn:
+<A6How to activate a light source for movement in a view;
*ACHow to use a light's directional vector to locate a light in space;
*A6How to create a new light source and add it to a view;
*A"How to center a light in the view;
*A%How to create and control spotlights;
*A&How to create and control area lights;
*A&How to define attenuation for a light;
How to enable shadow casting;
*A8How to use Shadow Map Size to control shadow resolution;
*A:How to use Self-Shadow Bias to fine-tune shadow location;
*A How to control shadow intensity;
*A1How to change the color and intensity of a light.
We'll start with a new project.
Restart Renderize Live EZ.
*A0Load "tutor6.eye" from the SIMPLY3D\EYESEZ\TUTOR
directory.
*A>Drag and drop "view1" into the viewport to make it the current
view.
t9This is the same as dropping the view into the View Well.
Set "Test:1" and select the
$ button to perform a quick-render of
    the view.
Locating and Positioning Lights
*cNIn Tutorial 2 we gained some exposure to the positioning of lights.  Let's now
review how this is done.
*AF"view1" contains one Point Light originating from behind and below the
*2Ocamera.  To view the position of the light we must first make the light active.
Tutorial 6: Working with Lights
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Select the
4 button on the Resource Manager to display the Light
Resource Palette.
*A*Drag and drop "light1" into the Move Well.
>>Figure 57. Activate a light by dropping it into the Move Well.
GThis brings up the Move Toolbox with "light1" active in the viewport.
*AKLight resources are not visible in the camera display, because they are not
*2Prendered entities.  Therefore, to position a light you must change to one of the
orthographic viewport displays.
Select the
1 button on the Command Bar to change the viewport
to a Side view.
JThe first consideration with lighting is the light's location in 3D space.
*2S"light1" is far from the display area, so the light source is not visible.  To find
*2Sthis light, let's first locate its directional vector by targeting the light at our
object.
Select the
0  button on the Target Location area of the Move
1Toolbox: this is used to select a light's target.
*A4Point to the center of the viewport and select once.
MNow we see a line running in from the right.  This is the light's directional
*2Tvector, indicating the general location of the light source.  Note that point lights
*2Pshine in all directions at once, and therefore the directional vector associated
*2Ewith them is not meaningful in terms of illumination.  However, these
*2Odirectional vectors are extremely useful for locating light sources in 3D space
*2;and visualizing the relative position of lights to objects.
*A,Now let's zoom out to find the light source.
Click on the
E' button on the Command Bar two times in
,succession to zoom out the viewport display.
PThe wireframe representation of the light source is now visible in the viewport.
Select the
- button to change to a 4-up viewport display.
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Tutorial 6: Working with Lights
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tJThe Top, Front and Side  viewport displays give us orthographic bird's eye
*2Pvantage points of the entire assemblage of components in a view: lights, objects
*2Pand camera.  Notice that the Side view is still the active view (it is displayed
*2Swith a red border), and it is still in its zoomed out mode.  Let's return it to its
normal, unzoomed display.
Select the
, button on the Command Bar to reset the Side
viewport display.
tLThis button allows you to reset the zoomed position to the default Renderize
*2NLive EZ position.  The Zoom buttons only affect the viewport that is currently
active.
*d)Blue and Yellow Directional Light Vectors
*PQLook at the "Top" mini viewport and notice that the light's directional vector is
*2Rblue.  The color of the vector serves to indicate the location of the active light
*2Krelative to the current orthographic view, and whether the light is shining
*2Qtowards the view or away.  If a light is positioned so that it shines back toward
*2Othe plane from which you are currently viewing it, to even the smallest degree,
*2Othen the light's directional vector appears blue. If the light is directed away
*2Hfrom this plane (shining away from you), then the vector appears yellow.
*ANLook at the "Side" mini viewport and note that the light's vector is coming up
*2Nfrom beneath the camera ever so slightly.  Since the "Top" viewport display is
*2Jlooking down from above the camera, the light vector is generally directed
*2Jtoward it, and therefore displayed in blue when viewed from that viewport.
Positioning New Lights
*cKWhen working with a newly created light, it is sometimes best to center the
*2Llight in the view, so that positioning it in space isn't a difficult ordeal.
*APFirst we'll add a new light to the view.  There are four ways we can do this: we
*2Lcan open the View Designer and drop the light in the Add Well like we did in
*2ITutorial 2; we can select the "Add to View" option from the pop-down menu
*2Kthat appears when we select on the resource with the right mouse button; we
*2Ocan drag the light resource and drop it over the current view in the View Well;
*2Ror we can drag the light resource and drop it directly into the viewport to add it
to the current view.
+xBDDrag the light "default" from the Light Resource Palette and drop it
*29into the Project Designer viewport to add it to the view.
tKRemember from Tutorial 2 that the "default" light source cannot be altered.
*2OTherefore, when we add it to the current view it automatically changes to a new
name, "default_1".
*A*Now let's position this light in 3D space.
Tutorial 6: Working with Lights
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@Drag and drop the light resource "default_1" into the Move Well.
Select the
4 button on the Command Bar to change to a Side view.
!From the Move Toolbox select the
 button to center the light at
the camera.
Select the
. button on the Light Location area of the Move
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DToolbox, then with the pointer in the viewport drag the light higher
above the camera.
Now we'll target the light.
Select the
/ button on the Target Location area of the Move
EToolbox, then with the pointer in the viewport point to the center of
the objects and select.
8The target vector of the light updates to this location.
Select the
3 button on the Command Bar to change to a Top view.
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Select the
. button on the Light Location area of the Move
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DToolbox, then with the pointer in the viewport drag the light to the
left of the camera.
Now we'll target the light.
Select the
/ button on the Target Location area of the Move
EToolbox, then with the pointer in the viewport point to the center of
the objects and select.
RThe target vector of the light updates to this location.  To target accurately you
*20must set the target in at least two ortho views.
*ADNow let's render our view again to see the effects of our new light.
Select the
- button on the Command Bar to open the Render
Toolbox.
Select the
" button to perform a quick-render.
ONotice how the addition of a light has changed the illumination of the rendered
view.
The Different Types of Lights
*cKFour distinct types of lights are supported in Renderize Live EZ. They are:
Point Light
C: This is the default light in Renderize Live EZ. It is like a bare
2light bulb, radiating light out in all directions.
Tutorial 6: Working with Lights
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Spot Light:
AA light emitting a focused cone of light in a targeted direction.
JThe cone of light may contain an area of brightly focused light surrounded
*2?by a drop off area in which the light fades from bright to dim.
Area Light:
9A large light source made up of multiple point lights and
!emitting light in all directions.
Area Spotlight:
/ An area light given spotlight characteristics.
t3Two additional properties can be set in each light:
Attenuation:
8 Gives the light rays a specified length. Beginning at a
Jspecified distance from the light source, light rays gradually become less
*2Hintense, until they dissipate altogether at a second specified distance.
Casts Shadow:
. Enables the light's ability to cast shadows.
tRLet's see how different light type's affect the illumination of objects in a view.
Select the
7 button to display the View Resource Palette, then drag
@and drop "view2" into the View Well to make it the current view.
Set "Test:1/2" and select the
 button on the Render Toolbox.
tRThe current light in this view, "test", is a simple point light.  It is positioned
*2Odirectly in front of the camera.  We'll change this to a spotlight, and see how
that affects the rendered view.
Select the
3 button to display the Light Resource Palette, then
>drag the light resource "test" and drop it into the Edit Well.
*A;Select the "Spotlight" option on the Light Designer window.
b2Figure 58. These Buttons determine the Light Type.
tHNotice that a pair of dials appear under the Spotlight area of the Light
*2MDesigner: these are used to set the "hot" and "soft" angles of the spotlight.
*2%We'll come back to these in a moment.
+xB<Select "Save" and confirm "Replace", then minimize the Light
*2    Designer.
tNThe resource icon for "test" now displays a spotlight icon.  Let's see how the
spotlight looks in wireframe.
+xB5Drag the light "test" and drop it into the Move Well.
Select the
1 button on the Command Bar to change the viewport
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to a Top view.
tPNotice the wireframe representation for the spotlight.  It has two sets of lines
*2Nemanating from it: the area within the inside set of lines represents the "hot
Tutorial 6: Working with Lights
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Qangle" where the light shines at its full intensity.  The area between the inside
*2Pand outside set of lines represents the "soft angle" where the light's intensity
*2Pfalls off gradually until it reaches zero intensity at the outside set of lines.
*A8Now we'll render the image to see the spotlight effects.
Select the
1  button on the Command Bar to display the Render
Toolbox.
Select the
1 button on the Render Toolbox to render the view.
&Now let's make the bright spot larger.
+xB:Re-open the Light Designer with the light resource "test".
*A/Change the Dial marked "Hot Angle" to about 15.
NFigure 59. The hot and soft angles of a spotlight are specified independently.
+cQ,Save the light "test" and confirm "Replace".
Minimize the Light Designer.
Select the
4  button on the Command Bar to change to a Top view.
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NNotice how the inside pair of vectors are wider now that we have increased the
*2$"Hot Angle" in the Light Designer.
*A@You can also change the Spot Angle dynamically, using the mouse.
Select the
+ button on the Command Bar to open the Move
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Toolbox.
Select the
5 button on the Attributes area of the Move Toolbox to
edit the light's spot angles.
*ABMove the pointer into the viewport and drag the mouse from left to
right.
ONotice the changes to both light angle vectors.  The readout on the status line
reports the new angles.
+xB%Set the "Hot Angle" back to about 15.
Select the
- button on the Command Bar to open the Render
Toolbox.
Select  the
1 button on the Render Toolbox to render the view.
 Notice how the spot has changed.
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Tutorial 6: Working with Lights
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Creating Area Lights
*c(Now let's take a look at the Area Light.
+xB:Re-open the Light Designer with the light resource "test".
*A:Select the Area Light option on the Light Designer window.
tRAn Area Light increases the size of the light source to distribute light intensity
*2Iover a broad area.  Imagine an Area Light as a box containing a number of
*2Oevenly sized, evenly distributed light sources, or "samples".  The intensity of
*2Lthe light is distributed evenly among the samples; therefore, increasing the
*2Onumber of samples will not make the light brighter.  Spreading the light over a
*23large area results in softer, more diffuse shadows.
*AKWhen you select the Area Light option, the Light Designer window updates to
*2@display three "Area Scale" type-ins and a dial marked "Samples".
IFigure 60. The size and distribution of an area light are user-definable.
+5QDIn the type-ins under "Area Scale" type in: X = 200, Y = 200, Z = 15
*2%and set the "# of Samples" dial to 4.
tNThe "Area Scale" sets the size of the area light box.  The "# of Samples" dial
*2:indicates the number of light sources to place in the box.
+xB$Select "Save" and confirm "Replace."
*A#Minimize the Light Designer window.
tBNotice that this light resource now updates to an area light icon.
Select the
1 button on the Command Bar to change to the front
viewport display.
Select the
0 button on the Command Bar to zoom the view out.
tLNotice the shape of this Area Light.  It appears as a large square from this
*2Oview.  In fact, this light is represented by a pizza shaped box. The dimensions
*2Oof this box were derived from the X, Y and Z "Area Scale" type-ins in the Light
*2NDesigner.  The "Samples" dial establishes the number of origins the Area Light
*2Nwill have.  We selected 4, so the light will be distributed among four sources
*2%positioned evenly throughout the box.
Select the
1 button on the Render Toolbox to render the view.
tMNotice that the rendering looks nearly the same as the rendering we made with
*2Vthe Point Light, except that the Light appears a little less bright.  It's less bright
*2Pbecause the same light energy is being divided into four light pieces and spread
*2Pover a greater area.  In other words, the power or intensity of an Area Light is
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Tutorial 6: Working with Lights
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Mdivided among the number of samples set: the intensity of the Area Light does
*2$not grow stronger with more samples.
*AKAn Area Spotlight is the combination of both an Area Light and a Spotlight.
*2JThe light is distributed over a specified area using a specified number of
*2Rsamples, but the light as a whole displays the drop-off characteristics associated
with a spotlight.
Creating an Attenuated Light
*cFFor rendering purposes, attenuation simply means diminishing a light's
*2Ointensity as the light beam travels farther from the source.  Renderize Live EZ
*2Qallows you to determine the distance a light beam travels before it begins losing
*2<intensity, and the point at which it reaches zero intensity.
+xB;Drag and drop the view resource "view3" into the View Well.
Select the
3 button on the Render Toolbox to render the current
view.
SThe light resource in this view, "point", is a simple point light. Let's make it an
attenuated light.
+xB:Drag and drop the light resource "point" in the Edit Well.
*A;Select the "Attenuate" option on the Light Designer window.
HTwo new dials appear in the Light Designer: "On Dist" and "Fade Dist".
LFigure 61. Set attenuation using the "On Distance"and "Fade Distance" dials.
NWe will be setting the "On Dist" and "Fade Dist" dials to numbers greater than
*2Rthe dials are capable of setting, so we'll need to change these dials to type-ins.
+xBDWith the cursor over the dial titles "On Dist" and "Fade Dist" click
with the right mouse button.
*AAIn the type-ins, enter 100 for "On Dist" and 160 for "Fade Dist".
*A$Select "Save" and confirm "Replace".
*A Close the Light Designer window.
PNotice the light resource icon for "point": it updates with "Atten" written onto
*2)the icon, indicating an attenuated light.
+xB<Drag and drop the light resource "point" into the Move Well.
Select the
/ button on the Command Bar to change to the top
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viewport display.
Tutorial 6: Working with Lights
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tNNotice the light's directional vector now has two markers.  The one closest to
*2Sthe light source marks the "On Distance": the light will be at full intensity until
*2Mit reaches this point.  The next marker represents "Fade Distance": the light
*2Ogradually loses intensity until it reaches an intensity of zero at this marker.
*AFWe can also set the attenuation distances dynamically using the mouse.
Select the
5 button on the Move Toolbox to modify the light's "On
Distance" marker.
*ADPosition the pointer in the viewport and drag to change the location
of the "On Distance" marker.
tHNotice that the "Fade Distance" marker moves also: this is because "Fade
*25Distance" is measured from the "On Distance" marker.
+xBCReplace the markers to an "On" distance of 100.  Look to the status
*2<line as you drag the marker to get a numeric read out of the
marker's placement.
tLNow we'll render the view again to see the effect that attenuation gives us.
Select the
0 button on the Command Bar to display the Render
Toolbox.
Select the
1 button on the Render Toolbox to render the view.
tJThe intensity of the light fades as it gets farther from the light source.
Creating Shadows
*cKUnlike lights in the real world, lights in Renderize Live EZ may or may not
*2Kcast shadows.  All lights can be individually controlled to cast shadows by
*29selecting the Cast Shadows option  in the Light Designer.
+xB)Drag and drop "view4" into the View Well.
Select the
4 button on the Options area of the Render Toolbox to
.enable the calculation and display of shadows.
tRBecause the calculation of shadows takes some time, it is often best to leave this
*2Pbutton disabled during the view creation process until you are ready to finalize
your lighting effects.
Select the
1 button on the Render Toolbox to render the view.
t6There appears to be only one shadow in the foreground.
+xB9Drag and drop light resource "light2" into the Move Well.
*ACInspect the position of the light, sphere and cube by selecting the
+B@4 button on the Command Bar and inspecting the views.
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Tutorial 6: Working with Lights
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LJudging from the position of "light2", it's obvious that the cube and sphere
*2Eshould cast shadows onto the back wall.  To make shadows appear, four
*27different settings need to be taken into consideration:
+<AGThe objects from which shadows are to be cast must be selected to "Cast
*2 Shadows" in the Object Designer.
*AHThe object on which shadows are to fall must be set to "Receive Shadows"
*2.in the Object Designer -- the default setting.
*AHThe lights which are to cast shadows must have the "Casts Shadow" option
selected in the Light Designer.
< button must be selected on the Render Toolbox to enable the
$computation and display of shadows..
OFirst let's check to see if the objects "sphere" and "cube" are defined to cast
*2;shadows and whether the backdrop is set to receive shadows.
+xB;Load the object resource "sphere" into the Object Designer.
*A>From the Object Designer, check to see that the "Cast Shadows"
button is selected.  It is.
*AALoad "cube" into the Object Designer.  It too is selected to Cast
Shadows.
*ABLoad "lwall" into the Object Designer and confirm that the Receive
Shadows button is selected.
Close the Object Designer.
ANow let's see if the lights in this view are set to cast shadows.
+xB5Load light resource "light2" into the Light Designer.
*AAFrom the Light Designer check to see if the "Cast Shadows" option
*22is selected.  It isn't selected, so select it now.
KNotice that two type-ins, "Shadow Bias" and "Shadow Map Size" appear on the
*21Light Designer, as well as an "Intensity" dial.
OFigure 62. Shadows are controlled using these selections in the Light Designer.
*P:We will explore these shadow control features in a moment.
+xB$Select "Save" and confirm "Replace".
PNotice that this light's icon now displays "Shad", indicating that this is now a
light which will cast a shadow.
+xB,Load light "light3" into the Light Designer.
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Tutorial 6: Working with Lights
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tOThis light is already casting a shadow.  This is the light that cast the shadow
*2.that we saw when we rendered the current view.
+xB&Load "light4" into the Light Designer.
*A!Select the "Cast Shadows" option.
*A$Select "Save" and confirm "Replace".
*A Close the Light Designer window.
Select the
0 button on the Command Bar to display the Render
Toolbox.
tNSince we are performing a rendering to examine our shadows, let's speed things
*23up by temporarily turning off all of our materials.
Select the
. button on the Resource Manager to display the
Material Resource Palette.
*AASelect the Materials pop-down directly above the Resource Palette
*2%and select the "Turn All Off" option.
JFigure 63. Turn resources off and on globally by selecting on the pop-down
above the Resource Palette.
tLAll materials will now be ignored during rendering.  Notice that each of the
*2Lmaterial icons in the Resource Palette has the word "OFF" written across it.
Now let's render.
Set "Test:1" and select the
 button to render the view.
tLNow shadows are calculated for each light, and the shadows are rendered with
*2    the view.
*AKBecause we were only interested in examining shadows, we temporarily turned
*2Roff all of our materials to speed up the rendering time.  In views where there are
*2HColor or Reflect Textures associated with the materials, the increase in
*2Krendering speed can be significant.  Use this ability to turn materials and
*2Mobjects on and off during rendering to speed up the iterative design process.
Setting Shadow Map Size
*cPTake a good look at the edges of the shadows: to change the edge definition of a
*2-shadow we need to change the shadow map size.
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Tutorial 6: Working with Lights
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&Load "light4" into the Light Designer.
*A=In the type-in titled "Shadow Map Size" enter the value "75".
*A$Save "light4" and confirm "Replace".
*A=Load "light3" into the Light Designer and set the "Shadow Map
Size" to "320".
*A$Select "Save" and confirm "Replace".
*A Close the Light Designer window.
3Before we render, let's turn our materials back on.
Select the
6 button to display the Material Resource Palette, then
?select on the Materials pop-down above the Resource Palette and
*2 choose the "Turn All On" option.
@Now our material definitions will be included in the rendering.
Select the
1 button on the Render Toolbox to render the view.
FNotice the improvement in the sharpness of the shadow edge in the left
*2Iforeground.  This is a shadow created by "light3", for which we increased
*2Fshadow map size to 320.  And notice how the shadows cast from "light4"
*2Fappear fuzzier: we set a smaller shadow map size, 75 for this light.
*ALIt is important to remember that the larger you set the shadow map size, the
*2Plonger it will take to render the view.  In addition, larger shadow maps require
*2Jmore memory to perform the rendering.  Generally, speaking, you should not
*2Lneed to set a shadow map size greater than 640.  However, if you are working
*2Mon a complex view in which objects are located well outside of the extants of
*2Mthe camera view, and these objects are set to cast shadows, then you may need
*2Dto increase the shadow map size above 640 to obtain crisp shadows.
Self Shadow Bias
*cIThe "Self Shadow Bias" type-in in the Light Designer is used to fine tune
*2Oshadows.  It uses a scale from 0 to 1 to determine the point at which an object
*2Qbegins casting a shadow.  Set to 0, an Object will cast a shadow onto itself.  At
*2P1 the object won't cast a shadow at all.  The Renderize Live EZ default value of
*240.1 should be a good starting place for most views.
*ANOptimum shadow bias is a mean setting.  Since every view is different, getting
*2Ua feel for balancing this setting is most useful.  It is first necessary to recognize
*2Aa few key visual clues indicating problems with your shadow bias.
+xB2Drag and drop the view "view5" into the View Well.
*A2Load the light "sunlight" into the Light Designer.
Set the Self Shadow Bias to 0.
*A&Save "sunlight" and confirm "Replace".
Tutorial 6: Working with Lights
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Minimize the Light Designer.
*A(Select "Test:1/2" on the Render Toolbox.
Select the
1 button on the Render Toolbox to render the view.
tMWhen Self Shadow Bias is set too low, objects will shadow themselves.  Notice
*2Mthe strange pattern appearing on the right wall of the building: we call this
*2Neffect "hashing".  If you see hashing on your object,  your Shadow Bias is set
Maximize the Light Designer.
*A!Set the Self Shadow Bias to 0.03.
Save and confirm "Replace".
Minimize the Light Designer.
Select the
1 button on the Render Toolbox to render the view.
tMWith Self Shadow Bias at .03 the shadows are just about there, but notice the
*2Mround poles going into the wall: they're not casting shadows at their origin.
*2JWhen the Self Shadow Bias is too high, shadows don't meet objects at their
origins.
*APWe still need to set Self Shadow Bias lower to close the gap.  But if we make it
*2'too low, we could begin to get hashing!
Maximize the Light Designer.
*A"Set the Self Shadow Bias to 0.005.
Save and confirm "Replace".
Minimize the Light Designer.
Set "Test:1" and select the
  button on the Render Toolbox to
render the view.
t"Now we've found the right balance.
*AJSometimes the balance may be difficult to establish.  Hashing may begin to
*2Poccur before the shadows meet their origin.  If this happens, try increasing the
Shadow Map Size.
*AGYou can also deal with the problem of hashing by disabling the "Receive
*2<Shadows" button for the object on which the hashing occurs.
Setting Shadow Density
*cOYou can change the strength of a shadow using the "Intensity" dial on the Light
*2    Designer.
Maximize the Light Designer.
*A+Find the "Intensity" dial and set it to .5.
Tutorial 6: Working with Lights
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Save and confirm "Replace".
Minimize the Light Designer.
Render Image at 1.
&Changing a Light's Color and Intensity
*c@The color and strength of a light source can also be controlled.
Maximize the Light Designer.
PThe Color/Intensity Well in the bottom-left corner of the Light Designer is used
*2/to change the color and intensity of the light.
+xBCPoint to the Color/Intensity Well and select to activate this Well.
Select the
, button on the Command Bar to open the Color
Toolbox.
IThe color swatch of the Color Toolbox now displays the color in the Light
*2)Designer's Color/Intensity Well -- white.
+xB6Select the "hsv" color palette from the Color Toolbox.
GNotice the color white's HSV values. You can read these below the color
*2Esliders. Hue =0, Saturation =0, and Value =1.  White has no color and
*21saturation but its value is as high as it can go.
+xB;Slide the bottom slider left so that the value reads ".40".
LNotice the color swatch and the Color/Intensity now appear dark gray:  we've
*2@lowered the color value from 1 to .40 to adjust light intensity.
+xBBNow change the light's Hue: set the Saturation to .5, then set the
*2AHue value to approximately 50 using the Color Toolbox's HSV color
*A<From the Light Designer select "Save" and confirm "Replace".
*A Close the Light Designer window.
Select the
0 button on the Command Bar to display the Render
Toolbox.
Select the
1 button on the Render Toolbox to render the view.
LNotice how changing the intensity and color of this light changes the entire
rendered effect.
Final Considerations
*cJThe time required to compute shadows during rendering may be considerable,
*2Kdepending on the total number of lights casting shadows in the view.  Other
Tutorial 6: Working with Lights
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tJfactors influencing speed include the total number of polygons set to cast
*2Nshadows, the size of the shadow maps, the number of attenuated lights, and the
number of area lights.
*AKRendering with shadows enabled will slow down the iterative design process.
*2KWe recommend that you build and light your view selectively, choosing which
*2Mobjects and lights should cast shadows. A floor for instance, need not cast a
*2Nshadow.  A general Light serving to illuminate the entire view may not need to
*2Mcast a shadow.  Finally, disable the "Compute Shadows" button to turn off all
*2>shadows in test renderings not requiring a display of shadows.
Tutorial 6: Working with Lights
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Notes
Tutorial 6: Working with Lights
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Visual Software, Inc.

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