Name: 工作坊（第 7 周）：構建球體和基於球體的形式 (WORKSHOP (Week 7): Construction of Spheres and Spherical-based forms)
Uploaded: 2024-10-13T17:17:27.000Z
Duration: 15 min 59 s

Hi again everyone in this video. I'm going to cover the fundamentals of constructing spheres and spherical forms

在本視頻中，大家又見面了。我將介紹構建球體和球形的基礎知識

We will have a look at how to fully construct a sphere in stages

我們將看看如何分階段完整地構建一個球體

But let's have a look at what makes a sphere look like it's in perspective

不過，讓我們來看看是什麼讓球體看起來像是在透視中吧

So here you can see we have six spheres drawn from different perspective angles

在這裡，你可以看到我們從不同的角度繪製了六個球體

The silhouette of the sphere of course is just a circle

But it's the contour lines that help communicate what perspective angle they're drawn from the contour lines are based on three intersecting ellipses and

等高線是基於三個相交的橢圓和一個相交的圓錐曲線繪製的。

You can see here me tracing off those ellipses. There's the first one there's the second one and

你可以看到我在描畫這些省略號。這是第一個，這是第二個，還有

And those ellipses are based on the intersection of three planes

So let's simplify this and just take a look at one sphere from one particular angle in order to

是以，讓我們簡化一下，只從一個特定的角度觀察一個球體，以便

Understand how to construct these things. So here I have two spheres and these spheres are sitting on a horizontal surface

瞭解如何構造這些東西。這裡我有兩個球體，這些球體位於一個水準面上

How do we know that they're sitting on a horizontal surface?

我們怎麼知道它們是坐在水準面上呢？

Well, if we have a look at our ellipse lying horizontally

那麼，如果我們看看水準放置的橢圓

The major axis is horizontal to our view that ellipse would be sitting in a square

在我們看來，主軸是水準的，橢圓將位於正方形中

That is horizontal and our minor axis is straight up and down vertical

這是水準軸，我們的小軸是直上直下的垂直軸

This particular drawing is showing that we are slightly above the sphere

Drawn closer to our eye level and what's the rule?

拉近到我們的視線水準，規則是什麼？

Well, the flatter the minor axis is the closer it is to the horizon line

那麼，小軸越扁平，就越接近地平線

So we're still using the same principles that we've learned about sketching ellipses in perspective

是以，我們仍然採用我們已經學到的透視橢圓素描的原則

So let's take the perspective angle of this sphere and I'm going to use it to show you how to fully construct

是以，讓我們從這個球體的透視角度出發，我將用它來向大家展示如何完整地構建

This sphere in stages using three intersecting planes

這個球體分階段使用三個相交平面

So here we have the redrawn sphere using color-coordinated contour lines

是以，我們在這裡使用顏色協調的輪廓線重新繪製了球體

To the right. This is the full construction of that sphere. You can see here. I've drawn a very light estimated perspective cube and

在右邊。這是球體的完整結構。你可以看到這裡。我畫了一個估計值很低的透視立方體，然後

It's important to have your proportions correct particularly of the square planes

正確的比例很重要，尤其是正方形平面的比例

That we know that the ellipses are going to sit inside

The more accurate your ellipses are going to be the more accurate the contour lines to indicate surface are going to be

橢圓越精確，表示表面的等高線就越精確

Now I've left out the major and minor axes from this sketch just to keep it cleaner but take note of the major axis of this red ellipse and

現在，為了使草圖更簡潔，我省略了主軸和次軸，但請注意這個紅色橢圓的主軸和次軸。

The minor axis is actually a line going to the left vanishing point on this green ellipse the major axis

小軸實際上是一條通向綠色橢圓左側消失點的直線。

Is 90 degrees to the minor axis and that minor axis is going to the right vanishing point

與小軸成 90 度，小軸指向右側的消失點

Of course our blue ellipse, which is a horizontal ellipse its minor axis is vertical and major axis is horizontal and 90 degrees to that minor axis and

當然，我們的藍色橢圓是一個水準橢圓，它的小軸是垂直的，主軸是水準的，與小軸成 90 度，而主軸與小軸成 90 度。

Just to clarify that here. I'm just showing the three

在此澄清一下。我只是展示了三個

Ellipses on their individual planes, and I've indicated the major and minor axis of each of those ellipses

橢圓在各自的平面上，我標出了每個橢圓的主軸和次軸

Vertical ellipse, which is this green one the minor axis would be going to the vanishing point to the right

垂直橢圓，也就是這個綠色的橢圓，小軸將指向右側的消失點

And on the left vertical plane, which is this red ellipse its minor axis would be going to the left

而在左邊的垂直面上，也就是這個紅色的橢圓，它的小軸會向左移動

Vanishing point and of course the horizontal ellipse, which is this blue one. We have the centerline which is vertical

消失點，當然還有水準橢圓，也就是這個藍色的橢圓。我們有垂直的中心線

That's your minor axis 90 degrees to that would be your major axis the view up here is the same construction, but without the full construction of the cube and

這裡的視圖是相同的結構，但沒有立方體的完整結構和

You can see that we've got the three intersecting planes and the ellipses that sit on those planes

你可以看到，我們有三個相交的平面和位於這些平面上的橢圓

We're going to use this view to help us construct

我們將使用該視圖來幫助我們構建

Radiused corners, so let's have a closer look at that

弧形邊角，讓我們來仔細看看吧

Firstly let's have a look at a cube that has radiused corners, and you can see this cube here

首先，讓我們來看看一個四角呈弧形的立方體。

Which started off with sharp edges and sharp corners has actually been rounded off with radiused corners

從最初的銳邊尖角，到現在的圓角弧面

Each of these images here are actually part of the construction of a sphere

這裡的每張圖片實際上都是球體結構的一部分

So this bottom corner here bottom left corner

This sketch doesn't show the construction of the far side top corner, but in fact if we joined all of these corners

這張草圖沒有顯示遠側頂角的構造，但事實上，如果我們將所有這些角連接起來

Together we would actually make up a sphere

The outer images shown here are basically each of these corners without the full construction

這裡顯示的外層圖片基本上是每一個沒有完整結構的角

So in heavier line weight that would be the object as a solid or the corner as a solid and of course light line work to show the internal construction of that edge

是以，在較重的線條重量中，物體是實心的，角落是實心的，當然還有輕線條，以顯示邊緣的內部結構。

Corner, and of course the far side right corner and again the bottom left corner

角，當然還有最邊上的右角和左下角

The bottom leading corner and the bottom right corner drawn without all of its construction

繪製的左下角和右下角不包括所有結構

So let's see how to construct each of these corners by using our early image showing the intersecting planes and ellipses

那麼，讓我們看看如何利用早期顯示相交平面和橢圓的影像來構造這些角吧

Okay, so here you can see I've digitally replicated the construction of a sphere

好了，在這裡你可以看到我用數字技術複製了一個球體的結構

Using the construction with the three planes and the ellipses and from this I'll show you how to construct

利用三個平面和橢圓的構造，我將向你展示如何構造

The radius corners on the top surface of this sphere

You can see there are four quarters or four quadrants on the top surface above that horizontal plane and each of those

你可以看到，在水平面上方的頂面上有四個刻度或四個象限，每個刻度或象限都是

Corners are actually little cubes and we can take the top left corner to construct this radius corner

角實際上是一個小方塊，我們可以取左上角來構造這個半徑角

There's the leading radius that part of the ellipse will also have that part of the horizontal ellipse

橢圓的前導半徑也是水準橢圓的前導半徑。

This part of the green ellipse on the right vertical side and

右側垂直方向上的綠色橢圓部分和

The radius of the circle to construct the far side radius corner we would take the far side cube

圓的半徑來構造遠側半徑角，我們將取遠側立方體

Define the base edge or the baseline edge

Trace off the sections of the ellipses on the left vertical face

在左側垂直面上描出橢圓的部分

Here we have the top right radius corner and it's basically the flip side of the top left radius corner

這裡是右上角半徑角，基本上是左上角半徑角的翻轉面

Again we trace off the vertical edge horizontal edge that part of the right vertical ellipse

同樣，我們從垂直邊緣的水準邊緣描出右側垂直橢圓的部分

This part of the left vertical ellipse it will tangent the radius of the circle

左側垂直橢圓的這一部分將與圓的半徑相切

Part of the horizontal ellipse and of course that should tangent smoothly to the perimeter of the circle itself or the sphere itself

水準橢圓的一部分，當然應該與圓本身或球體本身的周長平滑相切

And the last of the four radius corners on this top surface would be the forward facing radiused corner and you can see

頂面四個弧形角中的最後一個是朝前的弧形角，你可以看到

We're taking this section of the horizontal ellipse that section of the left

我們將水準橢圓的這一部分，即左側的那一部分

Vertical side ellipse and this section of the right

Vertical side ellipse and that's it. If I wanted to show the inside construction of each of these radius corners, of course, you can come in with lighter line weight and define these construction lines

垂直側橢圓，就是這樣。當然，如果我想顯示每個半徑角的內部結構，可以使用較輕的線條重量來定義這些結構線

So that's if we want to show all the internal construction

是以，如果我們想展示所有的內部結構

I'm using a finer point fineliner to do this and

我是用較細的細線筆畫的，而且

Obviously these aren't shown on the images on the top row here

很明顯，這裡最上面一排的圖片上沒有顯示這些內容

Okay, so let's now have a look at constructing the radius corners on the bottom surface of this sphere

好了，現在讓我們看看如何在球體底面上構建半徑角

Four little cubes and we trace off the edges and parts of the radius of these ellipses to construct our corner

四個小方塊，我們沿著這些橢圓的邊緣和部分半徑來構建我們的角

So with the bottom left radius corner, I'm tracing off

是以，在左下角的半徑角上，我將描畫出

That horizontal and vertical line it gives me a sharp edge and corner

這條橫線和豎線給我帶來了鮮明的稜角

Then of course, I'm going to trace off this section of the horizontal

當然，我還要把這部分水平線描畫出來。

Ellipse this part of the left vertical ellipse and here's the tangent which would be the outline or the perimeter of the circle

將左側垂直橢圓的這一部分橢圓化，這裡是切線，也就是圓的輪廓或周長

The far side lower radius corner which would be the box at the back of this lower surface we would see a leading corner

遠側的下半圓角，也就是下表面背面的方框，我們會看到一個引角

Then I would have this section of the yellow ellipse, which is that left vertical ellipse this section of the right vertical ellipse

然後，我將把這部分黃色橢圓，也就是左邊的垂直橢圓 這部分右邊的垂直橢圓

And of course that section of the horizontal ellipse

Moving along to the right side lower radius corner

I'm tracing off again an edge that I can see

Oops a little bit wonky and then I would see that this section of the top

哎呀，有點亂，然後我會看到頂部的這一部分

Vertical ellipse, which is the green one and of course the perimeter of the actual sphere itself and

垂直橢圓，也就是綠色的那個，當然還有實際球體本身的周長，以及

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工作坊（第 7 周）：構建球體和基於球體的形式 (WORKSHOP (Week 7): Construction of Spheres and Spherical-based forms)

perspective

slightly

basically

structure