Opengl 按给定方向缩放网格的一部分

我有很多立方体（ex 100），它们都是同一个网格的一部分，在顶点着色器中，我想沿给定轴缩放每个立方体，因此它的顶部移动，立方体拉伸如下：

layout (location = 0) in vec3 vertexPos;
layout (location = 1) in vec3 vertexNor;
layout (location = 2) in float vertexCubeId;

uniform mat4 mvp;

uniform vec3 cubeUps[100];
uniform vec3 cubeOrigins[100];

void main()
{
    int cubeIndex = int(vertexCubeId);
    vec3 cubeUp = cubeUps[cubeIndex];
    vec3 cubeOrigin = cubeOrigins[cubeIndex];

    vec3 transformedPos = vertexPos;

    transformedPos.x += cubeUp.x;
    transformedPos.y += cubeUp.y;
    transformedPos.z += cubeUp.z;

    gl_Position = mvp * vec4(transformedPos, 1.0);
}

...

float scaleFactor = 1.5f;
vec3 scale = cubeUp * scaleFactor;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

transformedPos.x *= scale.x;
transformedPos.y *= scale.y;
transformedPos.z *= scale.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

gl_Position = mvp * vec4(transformedPos, 1.0);

...

float scaleFactor = 1.5f;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

float dotProduct = dot(cubeUp, transformedPos);
dotProduct *= (scaleFactor - 1.0f);   // or just set scaleFactor
                                      // to 0.5f in the first place
vec3 offset = cubeUp * dotProduct;

transformedPos.x += offset.x;
transformedPos.y += offset.y;
transformedPos.z += offset.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

每个立方体都有一个

ID

，每个顶点都有一个相应的

ID

，因此每个顶点都知道它是哪个立方体的一部分。一个统一的vec3规格化立方体数组（立方体应扩展的方向）和一个统一的vec3立方体数组（每个立方体的底部）也传递给着色器。这些统一数组的索引与多维数据集的

ID

匹配

好的，我知道立方体的

cubeOrigins

像白点一样放在每个立方体底部的中心，因为我认为这是需要的，但不确定：

我可以很容易地沿着给定的

normal

转换立方体，如下所示：

layout (location = 0) in vec3 vertexPos;
layout (location = 1) in vec3 vertexNor;
layout (location = 2) in float vertexCubeId;

uniform mat4 mvp;

uniform vec3 cubeUps[100];
uniform vec3 cubeOrigins[100];

void main()
{
    int cubeIndex = int(vertexCubeId);
    vec3 cubeUp = cubeUps[cubeIndex];
    vec3 cubeOrigin = cubeOrigins[cubeIndex];

    vec3 transformedPos = vertexPos;

    transformedPos.x += cubeUp.x;
    transformedPos.y += cubeUp.y;
    transformedPos.z += cubeUp.z;

    gl_Position = mvp * vec4(transformedPos, 1.0);
}

...

float scaleFactor = 1.5f;
vec3 scale = cubeUp * scaleFactor;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

transformedPos.x *= scale.x;
transformedPos.y *= scale.y;
transformedPos.z *= scale.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

gl_Position = mvp * vec4(transformedPos, 1.0);

...

float scaleFactor = 1.5f;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

float dotProduct = dot(cubeUp, transformedPos);
dotProduct *= (scaleFactor - 1.0f);   // or just set scaleFactor
                                      // to 0.5f in the first place
vec3 offset = cubeUp * dotProduct;

transformedPos.x += offset.x;
transformedPos.y += offset.y;
transformedPos.z += offset.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

但是我的缩放计划没有成功。我认为我需要做的是：

从顶点减去原点，以使用顶点的公共基 缩放

以某种方式沿“cubeUp”向量进行缩放

将原点添加到顶点以再次远离基准

大概是这样的：

layout (location = 0) in vec3 vertexPos;
layout (location = 1) in vec3 vertexNor;
layout (location = 2) in float vertexCubeId;

uniform mat4 mvp;

uniform vec3 cubeUps[100];
uniform vec3 cubeOrigins[100];

void main()
{
    int cubeIndex = int(vertexCubeId);
    vec3 cubeUp = cubeUps[cubeIndex];
    vec3 cubeOrigin = cubeOrigins[cubeIndex];

    vec3 transformedPos = vertexPos;

    transformedPos.x += cubeUp.x;
    transformedPos.y += cubeUp.y;
    transformedPos.z += cubeUp.z;

    gl_Position = mvp * vec4(transformedPos, 1.0);
}

...

float scaleFactor = 1.5f;
vec3 scale = cubeUp * scaleFactor;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

transformedPos.x *= scale.x;
transformedPos.y *= scale.y;
transformedPos.z *= scale.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

gl_Position = mvp * vec4(transformedPos, 1.0);

...

float scaleFactor = 1.5f;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

float dotProduct = dot(cubeUp, transformedPos);
dotProduct *= (scaleFactor - 1.0f);   // or just set scaleFactor
                                      // to 0.5f in the first place
vec3 offset = cubeUp * dotProduct;

transformedPos.x += offset.x;
transformedPos.y += offset.y;
transformedPos.z += offset.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

但这会将立方体移动到不需要的位置，并且无法正确缩放它们

我是否需要在应用比例之前旋转顶点坐标，以便正确使用原点

---

如何从给定的

cubeUp

向量获得用于缩放的正确值？

在

cubeUp

方向上取顶点的点积（减去原点后），然后缩放并添加到顶点位置。这将确保顶点仅沿

cubeUp

的方向移动。大概是这样的：

layout (location = 0) in vec3 vertexPos;
layout (location = 1) in vec3 vertexNor;
layout (location = 2) in float vertexCubeId;

uniform mat4 mvp;

uniform vec3 cubeUps[100];
uniform vec3 cubeOrigins[100];

void main()
{
    int cubeIndex = int(vertexCubeId);
    vec3 cubeUp = cubeUps[cubeIndex];
    vec3 cubeOrigin = cubeOrigins[cubeIndex];

    vec3 transformedPos = vertexPos;

    transformedPos.x += cubeUp.x;
    transformedPos.y += cubeUp.y;
    transformedPos.z += cubeUp.z;

    gl_Position = mvp * vec4(transformedPos, 1.0);
}

...

float scaleFactor = 1.5f;
vec3 scale = cubeUp * scaleFactor;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

transformedPos.x *= scale.x;
transformedPos.y *= scale.y;
transformedPos.z *= scale.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

gl_Position = mvp * vec4(transformedPos, 1.0);

...

float scaleFactor = 1.5f;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

float dotProduct = dot(cubeUp, transformedPos);
dotProduct *= (scaleFactor - 1.0f);   // or just set scaleFactor
                                      // to 0.5f in the first place
vec3 offset = cubeUp * dotProduct;

transformedPos.x += offset.x;
transformedPos.y += offset.y;
transformedPos.z += offset.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

为了直观地理解为什么简单地乘以比例向量不起作用，请想象由

cubeOrigin

和

cubeUp

定义的平面上的顶点（即立方体的底部）。它不应该动。但是，每个角点顶点都将有一个非零的

transformedPos

向量，这意味着在乘以

scale

后，值将不相同，除非在特殊情况下，

cubeUp

正好指向X、Y或Z轴

---

您需要专门乘以

transformedPos

向量中位于

cubeUp

方向的部分，该部分等于

dot（cubeUp，transformedPos）*cubeUp

。与其先减去该部分，再乘以1.5，然后再重新相加，不如只乘以0.5再相加，效率更高。

vec3 cubeUp=cubeUps[popupIndex]；这应该是vec3 cubeUp=cubeUps[cubeIndex]？（和cubeOrigin一样）是的，你是对的，我现在就编辑它。感谢您的回答，我一到家就会查看解决方案：）